*Article* **Effect of TiO<sup>2</sup> Film Thickness on the Stability of Au<sup>9</sup> Clusters with a CrO<sup>x</sup> Layer**

**Abdulrahman S. Alotabi 1,2,3 , Yanting Yin 1,3, Ahmad Redaa 4,5 , Siriluck Tesana 6,7, Gregory F. Metha 8,\* ,† and Gunther G. Andersson 1,3,\* ,†**


**Abstract:** Radio frequency (RF) magnetron sputtering allows the fabrication of TiO<sup>2</sup> films with high purity, reliable control of film thickness, and uniform morphology. In the present study, the change in surface roughness upon heating two different thicknesses of RF sputter-deposited TiO<sup>2</sup> films was investigated. As a measure of the process of the change in surface morphology, chemically -synthesised phosphine-protected Au<sup>9</sup> clusters covered by a photodeposited CrO<sup>x</sup> layer were used as a probe. Subsequent to the deposition of the Au<sup>9</sup> clusters and the CrO<sup>x</sup> layer, samples were heated to 200 °C to remove the triphenylphosphine ligands from the Au<sup>9</sup> cluster. After heating, the thick TiO<sup>2</sup> film was found to be mobile, in contrast to the thin TiO<sup>2</sup> film. The influence of the mobility of the TiO<sup>2</sup> films on the Au<sup>9</sup> clusters was investigated with X-ray photoelectron spectroscopy. It was found that the high mobility of the thick TiO<sup>2</sup> film after heating leads to a significant agglomeration of the Au<sup>9</sup> clusters, even when protected by the CrO<sup>x</sup> layer. The thin TiO<sup>2</sup> film has a much lower mobility when being heated, resulting in only minor agglomeration of the Au<sup>9</sup> clusters covered with the CrO<sup>x</sup> layer.

**Keywords:** RF magnetron sputtering; TiO<sup>2</sup> film; morphology; triphenylphosphine; Au<sup>9</sup> ; gold clusters; photodeposition; CrOx; Cr(OH)<sup>3</sup> ; Cr2O<sup>3</sup> layer

#### **1. Introduction**

Titanium dioxide (TiO2) is a semiconductor widely used for a large range of photocatalytic applications and is also an ideal model system for various types of studies [1,2]. There are various techniques to prepare TiO<sup>2</sup> films, such as sol-gel [3], evaporation [4], chemical vapour deposition [5], atomic layer deposition [6] and radio frequency (RF) magnetron sputtering [7]. Each of these methods has advantages and disadvantages in regard to fabrication costs, uniformity of the film morphology, thermal stability, purity and preparation time. Therefore, the best method of choice for TiO<sup>2</sup> film preparation depends on which application the film will be used in.

Amongst the above-named methods, RF magnetron sputtering is known to produce high-purity TiO<sup>2</sup> films with uniform thickness, ease of use and strong film adhesion to the substrate [8]. The properties of these films are significantly impacted by the sputtering

**Citation:** Alotabi, A.S.; Yin, Y.; Redaa, A.; Tesana, S.; Metha, G.F.; Andersson, G.G. Effect of TiO<sup>2</sup> Film Thickness on the Stability of Au<sup>9</sup> Clusters with a CrO<sup>x</sup> Layer. *Nanomaterials* **2022**, *12*, 3218. https:// doi.org/10.3390/nano12183218

Academic Editor: Orion Ciftja

Received: 17 August 2022 Accepted: 9 September 2022 Published: 16 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

conditions, such as RF power, gas pressure, substrate type, substrate temperature and targetto-substrate distance [9–14]. For instance, it has been reported that control of TiO<sup>2</sup> film thickness is possible by modulating the deposition time and the gas sputtering pressure [15].

TiO<sup>2</sup> films prepared with the RF magnetron sputtering method can be amorphous or have a rutile, anatase, or brookite crystal structure. It is well known that the physical properties of TiO<sup>2</sup> films depend highly on the post-deposition treatment, including heat treatment conditions [16–18]. Çörekçi et al. reported that a correlation between heating treatment and surface morphology with different TiO<sup>2</sup> film thicknesses. It was observed that an increase in surface roughness and grain sizes occurred during heating depending on TiO<sup>2</sup> film thicknesses, which also increased with film thickness. This is because increasing temperatures transform TiO<sup>2</sup> from amorphous to anatase and then to rutile [17], and these phase transitions affect the surface morphology of the TiO<sup>2</sup> film, which includes the roughness and crystallinity of the surface [19].

The aim of this study is to investigate the influence of heat treatment on the surface morphology of RF sputter-deposited TiO<sup>2</sup> films with two different thicknesses, and the effect this has on size-specific Au clusters deposited on the surface. TiO<sup>2</sup> films have attracted interest as substrates for investigating the role of Au clusters as cocatalysts in photocatalysis [20,21]. In these studies, TiO<sup>2</sup> films had been heated as part of the sample preparation procedure. The change in morphology, including surface mobility, upon heating, can lead to agglomeration of the Au clusters. Understanding the change in surface morphology upon heating, thus, is important when using TiO<sup>2</sup> as a substrate for investigating the cocatalyst properties. In the present work, phosphine-protected Au<sup>9</sup> clusters covered by a photodeposited CrO<sup>x</sup> layer were used as probes for the TiO<sup>2</sup> mobility during the change of morphology upon heating. Scanning electron microscopy (SEM), X-ray diffraction (XRD), laser scanning confocal microscope (LSCM) and X-ray photoelectron spectroscopy (XPS), have been applied to characterise the thickness, crystal structure, surface morphology and chemical composition and size of the Au cluster. The importance of the present work is to show that morphology changes in RF sputter-deposited TiO<sup>2</sup> depend on the thickness of the TiO<sup>2</sup> layer, and that Au<sup>9</sup> clusters can be used to probe morphology changes in the surface.

#### **2. Experimental Methods and Techniques**

#### *2.1. Material and Sample Preparation*

#### 2.1.1. Preparation of TiO<sup>2</sup> Films

The RF magnetron sputtering method was used to prepare TiO<sup>2</sup> films on a silicon wafer under high vacuum conditions (HHV/Edwards TF500 sputter coater) [22]. Before the deposition, the silicon wafer was cleaned with ethanol and acetone and then dried in a stream of dry nitrogen. The TiO<sup>2</sup> film was deposited onto a p-type silicon wafer substrate by sputtering a 99.9% pure TiO<sup>2</sup> ceramic target with 500 W sputtering power using Ar<sup>+</sup> (flow rate of 5 sccm) for 50 min. The sputter coating chamber was held under vacuum at <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>5</sup> mbar. This process resulted in TiO<sup>2</sup> films formed on the silicon wafer with a native oxide layer of TiO2.

TiO<sup>2</sup> films with two different thickness were fabricated applying the above-described procedure. The TiO<sup>2</sup> films had different colours based on light interference [23]: a TiO2/Si wafer with a purple colour and a TiO2/Si wafer with a gold-like colour (see Figure S1). The difference in colour of the films is related to the difference in light interference patterns within the films due to their difference in film thickness [24]. The thickness of TiO2P is ~400 nm, while TiO2G is ~1100 nm (*vide infra*). The TiO<sup>2</sup> wafers were cut into 1 cm × 1 cm pieces and used without further treatment. The two TiO<sup>2</sup> wafers are hereafter referred to as (i) TiO2P and (ii) TiO2G.

#### 2.1.2. Deposition of Au<sup>9</sup> Clusters

The deposition procedure of Au9(PPh3)8(NO3)<sup>3</sup> (Au9) was identical for both the TiO2P and TiO2G samples. Phosphine-protected Au<sup>9</sup> clusters were synthesised as reported previously [25]. A UV-Vis spectrum of the Au<sup>9</sup> cluster is shown in Figure S2. The TiO<sup>2</sup> films were immersed in Au<sup>9</sup> methanol solutions (2 mL) for 30 min at concentrations of 0.006, 0.06 and 0.6 mM. The TiO<sup>2</sup> samples were rinsed by quickly dipping them into pure methanol and then dried in a stream of dry nitrogen. These samples are hereafter referred to as (i) TiO2P-Au<sup>9</sup> and (ii) TiO2G-Au9.

#### 2.1.3. Photodeposition of CrO<sup>x</sup> Layer

Photodeposition of the CrO<sup>x</sup> layer was the same for both TiO2-Au<sup>9</sup> samples (TiO2P-Au<sup>9</sup> and TiO2G-Au9). A 0.5 mM potassium chromate solution was prepared by dissolving K2CrO<sup>4</sup> (≥99%, Sigma-Aldrich) in deionised water. The TiO2-Au<sup>9</sup> samples were immersed into the K2CrO<sup>4</sup> solution (1 mL) and irradiated for 1 h using a UV LED (Vishay, VLMU3510- 365-130) with ~1 cm between the sample and the irradiation source. The UV LED had a radiant power of 690 mW at 365 nm wavelength. After photodeposition, the samples were washed by dipping them into deionised water and dried in a stream of dry nitrogen [26]. These samples are hereafter referred to as (i) TiO2P-Au9-CrO<sup>x</sup> and (ii) TiO2G-Au9-CrOx.

#### 2.1.4. Heat Treatment

To remove the phosphine ligands from Au<sup>9</sup> clusters, all samples were treated with heating at 200 °C for 10 min under ultra-high vacuum (1 <sup>×</sup> <sup>10</sup>−<sup>8</sup> mbar) in the XPS chamber.

#### *2.2. Characterization Methods*

#### 2.2.1. Scanning Electron Microscopy and Energy Dispersive X-ray Spectroscopy (SEM-EDAX)

The thickness of TiO<sup>2</sup> films (TiO2P and TiO2G) was determined by combining SEM imaging and SEM-EDAX (FEI Inspect F50 microscope) scans on cross-sections of the TiO<sup>2</sup> samples. Cross-sectional images were recorded at a magnification of up to 100 k with 15 keV electron energy.

#### 2.2.2. X-ray Diffraction (XRD)

The crystal and phase structure of the TiO<sup>2</sup> films (TiO2P and TiO2G) before and after heating were analysed using XRD. A Bruker D8 Advance apparatus was used to record the XRD patterns with an irradiation source of Co-Kα (λ = 1.789 Å) operating at 35 kV and 28 mA.

#### 2.2.3. Laser Scanning Confocal Microscope (LSCM)

The surface morphology of TiO<sup>2</sup> films (TiO2P and TiO2G) was measured using a LSCM (Olympus LEXT OLS5000-SAF 3D LSCM) with 100x/0.80NA and 50x/0.60NA LEXT objective lenses. The Olympus Data Analysis software was used to calculate the arithmetic mean deviation (Ra) and root mean square deviation (Rq) values.

#### 2.2.4. X-ray Photoelectron Spectroscopy (XPS)

XPS analysis was performed using an X-ray source with Mg Kα line (hv = 1253.6 eV). A detailed description of the equipment has been given previously [27]. Survey spectrum scans were performed with a pass energy of 40 eV using a SPECS PHOIBOS-HSA 3500 hemispherical analyser. High-resolution XPS spectra were recorded for C, O, P, Si, Ti, Cr and Au with a pass energy of 10 eV. All XPS binding energy scales were normalised using the C 1 s peak at 285 eV. The peaks were fitted to calculate relative intensities considering atomic sensitivity factors. XPS was recorded immediately after sample preparation and heating, thus, reducing the number of atmospheric exposures.

#### **3. Results and Discussion**

#### *3.1. Influence of the Thickness of the TiO<sup>2</sup> Films*

The influence of the thickness of the RF sputter-deposited TiO<sup>2</sup> on the change in film morphology upon heating is investigated. First, we will determine the thickness of the TiO<sup>2</sup> films for TiO2P and TiO2G and describe the crystallinity and morphology of both samples before and after heating. Then, the XPS results will be reported for both TiO2P and

TiO2G. Subsequently, the agglomeration of Au<sup>9</sup> clusters beneath a Cr2O<sup>3</sup> overlayer upon heating of the two films is determined and discussed. and TiO2G. Subsequently, the agglomeration of Au<sup>9</sup> clusters beneath a Cr2O<sup>3</sup> overlayer upon heating of the two films is determined and discussed.

The influence of the thickness of the RF sputter-deposited TiO<sup>2</sup> on the change in film morphology upon heating is investigated. First, we will determine the thickness of the TiO<sup>2</sup> films for TiO2P and TiO2G and describe the crystallinity and morphology of both samples before and after heating. Then, the XPS results will be reported for both TiO2P

and Au with a pass energy of 10 eV. All XPS binding energy scales were normalised using the C 1 s peak at 285 eV. The peaks were fitted to calculate relative intensities considering atomic sensitivity factors. XPS was recorded immediately after sample preparation and

#### *3.2. Determination of the TiO<sup>2</sup> Film Thickness 3.2. Determination of the TiO<sup>2</sup> Film Thickness*

*3.1. Influence of the Thickness of the TiO<sup>2</sup> Films*

**3. Results and Discussion**

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 4 of 13

heating, thus, reducing the number of atmospheric exposures.

Figure 1 shows cross-section SEM images of TiO2P and TiO2G with line measurements of the thickness of the TiO<sup>2</sup> films. These SEM images clearly show that the thickness of the film for the TiO2P and TiO2G samples is ~400 nm and ~1100 nm, respectively; the film thickness of TiO2G is more than two times greater than for TiO2P. To confirm the film thickness, EDAX was further processed at the same image spots as SEM. Cross-section SEM-EDAX elemental maps of Ti, O and Si of TiO2P and TiO2G are shown in Figure S3. The EDAX elemental maps confirm that the thickness of the TiO<sup>2</sup> film for TiO2G is larger than for TiO2P. Figure 1 shows cross-section SEM images of TiO2P and TiO2G with line measurements of the thickness of the TiO<sup>2</sup> films. These SEM images clearly show that the thickness of the film for the TiO2P and TiO2G samples is ~400 nm and ~1100 nm, respectively; the film thickness of TiO2G is more than two times greater than for TiO2P. To confirm the film thickness, EDAX was further processed at the same image spots as SEM. Cross-section SEM-EDAX elemental maps of Ti, O and Si of TiO2P and TiO2G are shown in Figure S3. The EDAX elemental maps confirm that the thickness of the TiO<sup>2</sup> film for TiO2G is larger than for TiO2P.

**Figure 1.** Cross-section SEM images of the (**A**) TiO2P [28] and (**B**) TiO2G layer. **Figure 1.** Cross-section SEM images of the (**A**) TiO2P [28] and (**B**) TiO2G layer.

#### *3.3. Crystal Structure of the TiO2P and TiO2G before and after Heating 3.3. Crystal Structure of the TiO2P and TiO2G before and after Heating*

To assess the crystal structure of the TiO<sup>2</sup> film for TiO2P and TiO2G, XRD was conducted (Figure 2). There are no observable anatase, rutile or brookite crystal phase peaks [29], indicating that the films have an amorphous crystal structure. The crystallographic state of the TiO<sup>2</sup> is known to be transformed upon heating. The XRD patterns of TiO<sup>2</sup> films (TiO2P and TiO2G) after heating at 200 °C for 10 min are shown in Figure 2. Both spectra show an anatase peak at 29.8°, which confirms that the crystal structure of TiO2P and TiO2G has changed to the anatase phase after heating. The intensity of the anatase diffraction peak for TiO2G is more than two times higher than for TiO2P, which is due to the difference in the total amount of TiO<sup>2</sup> in each film. The TiO2G layer is more than two times thicker than TiO2P, so we also expect that there is more than twice as much anatase in the TiO2G film. Thus, the percentage change in crystal structure in the films is comparable. The formation of the anatase phase strongly suggests the TiO<sup>2</sup> film could be mobile during To assess the crystal structure of the TiO<sup>2</sup> film for TiO2P and TiO2G, XRD was conducted (Figure 2). There are no observable anatase, rutile or brookite crystal phase peaks [29], indicating that the films have an amorphous crystal structure. The crystallographic state of the TiO<sup>2</sup> is known to be transformed upon heating. The XRD patterns of TiO<sup>2</sup> films (TiO2P and TiO2G) after heating at 200 ◦C for 10 min are shown in Figure 2. Both spectra show an anatase peak at 29.8◦ , which confirms that the crystal structure of TiO2P and TiO2G has changed to the anatase phase after heating. The intensity of the anatase diffraction peak for TiO2G is more than two times higher than for TiO2P, which is due to the difference in the total amount of TiO<sup>2</sup> in each film. The TiO2G layer is more than two times thicker than TiO2P, so we also expect that there is more than twice as much anatase in the TiO2G film. Thus, the percentage change in crystal structure in the films is comparable. The formation of the anatase phase strongly suggests the TiO<sup>2</sup> film could be mobile during the heating process, which could influence the morphology of the TiO<sup>2</sup> films, as will be discussed below.

#### *3.4. Morphology of the TiO2P and TiO2G Layer before and after Heating*

LSCM was conducted on both TiO<sup>2</sup> films before and after heating to compare their morphology. Figure 3 shows the surface morphology of TiO2P and TiO2G before and after heating over an area of 16 × 16 µm and the determined Ra and Rq values. The 3D profiles of the same spots are displayed in Figure S4. Before heating, the Ra (and Rq) values of the TiO2P and TiO2G are 0.6 nm (0.8 nm) and 1.0 nm (1.3 nm), respectively. However, after heating, the values become 1.0 nm (1.2 nm) and 12.7 nm (14.7 nm), respectively. The change in Ra (and Rq) for TiO2P is small after heating, especially in comparison to TiO2G, which is 12 times higher after heating. The Ra (and Rq) values were also calculated over a much larger area of 595 × 595 µm and show a similar change (Figure S5). The change in the Ra

(and Rq) values indicates that both the TiO2P and TiO2G increase in surface roughness after heating. The XRD results show that the TiO2G and TiO2P have the same fraction of anatase after heating, so the total amount of anatase in TiO2G is larger compared to TiO2P (vide supra). Çörekçi et al. noted a similar finding in their study of different thicknesses of TiO<sup>2</sup> films heated at different temperatures [19]. The authors reported that the surface roughness of the thicker TiO<sup>2</sup> film (300 nm) increased more compared to thinner films (220 and 260 nm) upon heating. In our study, a large change in the surface roughness was observed clearly with the thicker film (more than two times thicker) by a factor of six. Çörekçi et al. assumed that the increase in surface roughness was due to increases in the grain sizes with increasing film thickness and the recrystallization in the TiO<sup>2</sup> films during heating. A number of studies have reported comparable findings that the surface morphology of the TiO<sup>2</sup> films changes upon heating [17,30]. Thus, we conclude that the thicker TiO2G film is more mobile during heating in comparison to the thinner film in the TiO2P sample. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 5 of 13 the heating process, which could influence the morphology of the TiO<sup>2</sup> films, as will be discussed below.

**Figure 2.** XRD patterns of the Si wafer, TiO2P and TiO2P after heating, TiO2G and TiO2G after heating to 200 °C. The positions of the diffraction peaks for anatase, rutile and brookite, as well as Si, are indicated using the standard XRD patterns (anatase PDF 01-075-1537, rutile PDF 01-071-4809, brookite PDF 04-007-0758 and Si PDF 00-013-0542). **Figure 2.** XRD patterns of the Si wafer, TiO2P and TiO2P after heating, TiO2G and TiO2G after heating to 200 ◦C. The positions of the diffraction peaks for anatase, rutile and brookite, as well as Si, are indicated using the standard XRD patterns (anatase PDF 01-075-1537, rutile PDF 01-071-4809, brookite PDF 04-007-0758 and Si PDF 00-013-0542).

#### *3.5. Au<sup>9</sup> Clusters on TiO2P and TiO2G; a Probe for Mobility during Heating*

*3.4. Morphology of the TiO2P and TiO2G Layer before and after Heating* LSCM was conducted on both TiO<sup>2</sup> films before and after heating to compare their morphology. Figure 3 shows the surface morphology of TiO2P and TiO2G before and after heating over an area of 16 × 16 µm and the determined Ra and Rq values. The 3D profiles of the same spots are displayed in Figure S4. Before heating, the Ra (and Rq) values of the TiO2P and TiO2G are 0.6 nm (0.8 nm) and 1.0 nm (1.3 nm), respectively. However, after heating, the values become 1.0 nm (1.2 nm) and 12.7 nm (14.7 nm), respectively. The change in Ra (and Rq) for TiO2P is small after heating, especially in comparison to TiO2G, which is 12 times higher after heating. The Ra (and Rq) values were also calculated over a In order to provide insight into the mobility of the TiO<sup>2</sup> during the recrystallisation process, Au<sup>9</sup> clusters were deposited onto the TiO<sup>2</sup> films and analysed with XPS. XPS was used to investigate the size of phosphine-protected Au<sup>9</sup> clusters deposited onto TiO2P and TiO2G. In addition, the effect of the CrO<sup>x</sup> overlayer on the Au<sup>9</sup> clusters was investigated, also with XPS. Figures 4 and 5 show the peak positions and relative intensities of Au 4f7/2 peaks in the XP spectra of three different concentrations (0.006, 0.06 and 0.6 mM) of TiO2P-Au9, TiO2G-Au9, TiO2P-Au9-CrO<sup>x</sup> and TiO2G-Au9-CrO<sup>x</sup> before and after heating. Tables S1 and S2 show a summary of all the Au 4f7/2 peak positions and full-width-half-maximum (FWHM). Note that all the Au 4f spectra for both substrates (TiO2P and TiO2G) are shown in Figures S6 and S7. The TiO2P XPS results will be first presented, followed by the TiO2G results.

much larger area of 595 × 595 µm and show a similar change (Figure S5). The change in the Ra (and Rq) values indicates that both the TiO2P and TiO2G increase in surface roughness after heating. The XRD results show that the TiO2G and TiO2P have the same fraction of anatase after heating, so the total amount of anatase in TiO2G is larger compared to TiO2P (vide supra). Ç örekçi et al. noted a similar finding in their study of different thicknesses of TiO<sup>2</sup> films heated at different temperatures [19]. The authors reported that the

films (220 and 260 nm) upon heating. In our study, a large change in the surface roughness was observed clearly with the thicker film (more than two times thicker) by a factor of six. Ç örekçi et al. assumed that the increase in surface roughness was due to increases in the grain sizes with increasing film thickness and the recrystallization in the TiO<sup>2</sup> films during heating. A number of studies have reported comparable findings that the surface morphology of the TiO<sup>2</sup> films changes upon heating [17,30]. Thus, we conclude that the thicker TiO2G film is more mobile during heating in comparison to the thinner film in the TiO2P

sample.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 6 of 13

**Figure 3.** Surface morphology with the Ra and Rq values of (**A**) TiO2P before heating and (**B**) TiO2P after heating, (**C**) TiO2G before heating and (**D**) TiO2G after heating (area 16 × 16 µm). Note that the scale bars are different. *3.5. Au<sup>9</sup> Clusters on TiO2P and TiO2G; a Probe for Mobility during Heating* **Figure 3.** Surface morphology with the Ra and Rq values of (**A**) TiO2P before heating and (**B**) TiO2P after heating, (**C**) TiO2G before heating and (**D**) TiO2G after heating (area 16 × 16 µm). Note that the scale bars are different. remain non-agglomerated clusters with CrO<sup>x</sup> coverage (see Scheme 1A). It is important to note that there is a decrease in Au intensity after photodeposition of the CrO<sup>x</sup> layer due to the coverage of Au<sup>9</sup> clusters (Figure 4D). These results are in agreement with our previous report showing that CrO<sup>x</sup> overlayers inhibit the agglomeration of Au clusters [28].

and there is no further decrease in the Au relative intensities, indicating that Au clusters

**Figure 4.** XPS results of TiO2P-Au<sup>9</sup> for three different Au<sup>9</sup> concentrations: (**A**) position of Au 4f7/2 and (**B**) relative intensity of Au before and after heating. TiO2P-Au9-CrO<sup>x</sup> (**C**) position of Au 4f7/2 and (**D**) relative intensity of Au before and after photodeposition of the CrO<sup>x</sup> layer and after heating. Note that the vertical scales of (**B**,**D**) are different and that the samples in (**A**,**C**) are different but are prepared in the same manner. **Figure 4.** XPS results of TiO2P-Au<sup>9</sup> for three different Au<sup>9</sup> concentrations: (**A**) position of Au 4f7/2 and (**B**) relative intensity of Au before and after heating. TiO2P-Au<sup>9</sup> -CrO<sup>x</sup> (**C**) position of Au 4f7/2 and (**D**) relative intensity of Au before and after photodeposition of the CrOx layer and after heating. Note that the vertical scales of (**B**,**D**) are different and that the samples in (**A**,**C**) are different but are prepared in the same manner.

**Figure 5.** XPS results of Au<sup>9</sup> deposited on TiO2G for three different Au<sup>9</sup> concentrations: (**A**) position of Au 4f7/2 and (**B**) relative intensity of Au before and after heating. TiO2G-Au<sup>9</sup> with the CrO<sup>x</sup> layer: (**C**) position of Au 4f7/2 and (**D**) relative intensity of Au before and after photodeposition of the CrO<sup>x</sup> layer and after heating. Note that the vertical scales of (**B**,**D**) are different and that the samples in (**A**,**C**) are different but are prepared in the same manner. **Figure 5.** XPS results of Au<sup>9</sup> deposited on TiO2G for three different Au<sup>9</sup> concentrations: (**A**) position of Au 4f7/2 and (**B**) relative intensity of Au before and after heating. TiO2G-Au<sup>9</sup> with the CrO<sup>x</sup> layer: (**C**) position of Au 4f7/2 and (**D**) relative intensity of Au before and after photodeposition of the CrO<sup>x</sup> layer and after heating. Note that the vertical scales of (**B**,**D**) are different and that the samples in (**A**,**C**) are different but are prepared in the same manner.

#### The chemical state of the phosphorous ligands of TiO2G-Au<sup>9</sup> without and with the *3.6. XPS of TiO2P Sample*

CrO<sup>x</sup> layer, both before and after heating, was determined using the P 2p region (see Figure S10 for more information and accompanying text). Figure S11 shows the Cr 2p spectra for TiO2G-Au9-CrO<sup>x</sup> before and after heating of the three different concentrations. All the Cr 2p3/2 peak positions are given in Table S4 and the peak positions are discussed in the supplementary section. *3.8. Effect of the TiO<sup>2</sup> Film Thickness* The protective effect of the CrO<sup>x</sup> layer on the agglomeration of Au<sup>9</sup> clusters is not the same for both the TiO2P and TiO2G substrates. The agglomeration of Au<sup>9</sup> clusters is inhibited on TiO2P with the CrO<sup>x</sup> overlayer but not on TiO2G, which shows a higher degree of agglomeration. The coverage of the CrO<sup>x</sup> layer on Au<sup>9</sup> clusters for both substrates is demonstrated by the decrease in the Au-XPS intensities. After heating, it is observed that the relative amount of CrO<sup>x</sup> decreases for both films (Table S5). Our previous studies on a similar system revealed that the CrO<sup>x</sup> layer diffuses into a TiO<sup>2</sup> film after heating to 600 ℃ due to the differences in surface energy between TiO<sup>2</sup> and CrO<sup>x</sup> [26]. In this study, both films were heated to only 200 ℃, however, CrO<sup>x</sup> on TiO2G experienced more diffusion of CrO<sup>x</sup> into the film compared to TiO2P. One possibility for the higher degree of Au<sup>9</sup> agglomeration and CrO<sup>x</sup> diffusion is the mobility of the TiO<sup>2</sup> film. Cluster agglomeration can be due to either (i) growth of the clusters over the surface or (ii) mobility of the substrate. In the case of (i), the cluster growth and agglomeration on a substrate can be ascribed to either Smoluchowski ripening or Ostwald ripening mechanisms. For Smoluchowski ripening, the agglomeration of clusters is caused by the collision and coalescence of entire Without the CrO<sup>x</sup> layer and before heating, the Au 4f7/2 peaks appeared at 85.1–85.4 eV with an FWHM of 1.7–1.8 eV (Figure 4A), whereas after heating, the Au 4f7/2 peaks shifted to slightly lower binding energies (84.7–84.8 eV) and FWHM (1.5–1.6 eV), and also showed a decrease in relative Au intensity across all Au<sup>9</sup> concentrations (Figure 4B). The results of the samples covered with a CrO<sup>x</sup> layer are shown in Figure 4C,D. The Au 4f7/2 peak positions of TiO2P-Au<sup>9</sup> after CrO<sup>x</sup> deposition but before heating were observed at 85.3 eV and an FWHM of 1.6 eV for all three concentrations. Note that the Au relative intensities decrease after the photodeposition of the CrO<sup>x</sup> layer, confirming the coverage of Au clusters with the CrO<sup>x</sup> layer (Figure 4D). After heating, the XPS peak position decreases slightly to 85.0 eV with no significant change in FWHM. The relative Au intensities also remained unchanged upon heating. XPS has been shown previously to be a reliable indicator of the size of phosphineprotected Au<sup>9</sup> clusters through the final state effect [21,28,31–36]. Generally, non-agglomerated Au<sup>9</sup> clusters on TiO<sup>2</sup> appear at a high binding peak (HBP) between 85.0–85.4 eV with an FWHM of 1.7 ± 0.2 eV, and agglomerated Au<sup>9</sup> clusters shift toward a low binding peak (LBP) at 84 eV with a decreasing FWHM that corresponds to bulk Au [28,31–35]. This XPS interpretation has been confirmed by correlating the XPS results with other techniques, such as HRTEM [33,34]. Here, the Au 4f7/2 peak positions of TiO2P-Au<sup>9</sup> without the CrO<sup>x</sup> layer after heating indicate a small degree of agglomeration of the Au<sup>9</sup> clusters for all concentrations. This is further confirmed by a small decrease in Au intensity after heating, indicating that some of the gold is attenuated due to some larger, agglomerated particles. Electrons emitted from the part of the clusters facing toward the substrate are attenuated when leaving the sample, which decreases the overall Au intensity [31,32]. Therefore, the same total amount of gold

deposited on the surface will have a lower intensity for large gold particles than that of small gold clusters. In contrast to the CrO<sup>x</sup> layer of the Au 4f7/2 peaks, positions are unchanged after heating and there is no further decrease in the Au relative intensities, indicating that Au clusters remain non-agglomerated clusters with CrO<sup>x</sup> coverage (see Scheme 1A). It is important to note that there is a decrease in Au intensity after photodeposition of the CrO<sup>x</sup> layer due to the coverage of Au<sup>9</sup> clusters (Figure 4D). These results are in agreement with our previous report showing that CrO<sup>x</sup> overlayers inhibit the agglomeration of Au clusters [28]. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 8 of 13

**Scheme 1.** Schematic illustration of the experimental procedure for preparing (**A**) TiO2P-Au9-CrO<sup>x</sup> and (**B**) TiO2G-Au9-CrOx. **Scheme 1.** Schematic illustration of the experimental procedure for preparing (**A**) TiO2P-Au<sup>9</sup> -CrOx and (**B**) TiO2G-Au<sup>9</sup> -CrOx.

The P 2p spectra of TiO2P-Au<sup>9</sup> without and with the CrO<sup>x</sup> layer before and after heating are shown in Figure S8 and the peak positions are discussed in the supplementary section. The Cr 2p spectra for TiO2P-Au9-CrO<sup>x</sup> before and after heating at the three different concentrations are shown in Figure S9. A summary of all the Cr 2p3/2 peak positions is shown in Table S3 and the peak positions are discussed in the supplementary section. The P 2p spectra of TiO2P-Au<sup>9</sup> without and with the CrO<sup>x</sup> layer before and after heating are shown in Figure S8 and the peak positions are discussed in the Supplementary Section. The Cr 2p spectra for TiO2P-Au9-CrO<sup>x</sup> before and after heating at the three different concentrations are shown in Figure S9. A summary of all the Cr 2p3/2 peak positions is shown in Table S3 and the peak positions are discussed in the Supplementary Section.

#### *3.7. XPS of TiO2G Sample 3.7. XPS of TiO2G Sample*

For the thicker film, TiO2G-Au9, the Au 4f7/2 peak positions before heating for all three different concentrations appeared at the HBP at 85.3 ± 0.1 eV (Figure 5A) and an FWHM of 1.8 ± 0.2 eV, corresponding to non-agglomerated Au clusters. However, after heating, the Au 4f7/2 shifted toward lower energy (84.6–84.9 eV) and an FWHM of 1.5–1.7 eV with a decrease in Au intensity (Figure 5B), indicating that Au clusters are partially agglomerated. With the CrO<sup>x</sup> layer deposited before heating, the Au 4f7/2 peak positions are observed at the HBP position at 85.3–85.5 eV (Figure 5C), with a decrease in Au 4f7/2 intensity due to the coverage of the CrO<sup>x</sup> layer on Au<sup>9</sup> clusters (Figure 5D). There is a slight increase in the binding energy of the Au 4f peak after the photodeposition of CrOx, and we do not know if this is a significant change or not. However, the position found can be used as an indication of the presence of non-agglomerated Au clusters. With the CrO<sup>x</sup> layer after heating, the Au 4f7/2 peak positions have further shifted to lower energy (84.3–84.8 eV) positions and an FWHM of 1.3–1.8 eV with a decrease in Au intensity, which is attributed to further agglomeration of the Au clusters based on the final state effect (see Scheme 1B). The degree of agglomeration increases with increasing Au<sup>9</sup> concentration for both cases (without and with the CrO<sup>x</sup> layer). Note here the difference; Au clusters on the surface of TiO2G undergo increased agglomeration after heating, even in the presence of the CrO<sup>x</sup> layer. This is different to the TiO2P, where Au clusters are less likely to agglomerate under For the thicker film, TiO2G-Au9, the Au 4f7/2 peak positions before heating for all three different concentrations appeared at the HBP at 85.3 ± 0.1 eV (Figure 5A) and an FWHM of 1.8 ± 0.2 eV, corresponding to non-agglomerated Au clusters. However, after heating, the Au 4f7/2 shifted toward lower energy (84.6–84.9 eV) and an FWHM of 1.5–1.7 eV with a decrease in Au intensity (Figure 5B), indicating that Au clusters are partially agglomerated. With the CrO<sup>x</sup> layer deposited before heating, the Au 4f7/2 peak positions are observed at the HBP position at 85.3–85.5 eV (Figure 5C), with a decrease in Au 4f7/2 intensity due to the coverage of the CrO<sup>x</sup> layer on Au<sup>9</sup> clusters (Figure 5D). There is a slight increase in the binding energy of the Au 4f peak after the photodeposition of CrOx, and we do not know if this is a significant change or not. However, the position found can be used as an indication of the presence of non-agglomerated Au clusters. With the CrO<sup>x</sup> layer after heating, the Au 4f7/2 peak positions have further shifted to lower energy (84.3–84.8 eV) positions and an FWHM of 1.3–1.8 eV with a decrease in Au intensity, which is attributed to further agglomeration of the Au clusters based on the final state effect (see Scheme 1B). The degree of agglomeration increases with increasing Au<sup>9</sup> concentration for both cases (without and with the CrO<sup>x</sup> layer). Note here the difference; Au clusters on the surface of TiO2G undergo increased agglomeration after heating, even in the presence of the CrO<sup>x</sup> layer. This is different to the TiO2P, where Au clusters are less likely to agglomerate under the CrO<sup>x</sup> layer after heating. This difference will be further discussed below.

the CrO<sup>x</sup> layer after heating. This difference will be further discussed below. The chemical state of the phosphorous ligands of TiO2G-Au<sup>9</sup> without and with the CrO<sup>x</sup> layer, both before and after heating, was determined using the P 2p region (see Figure S10 for more information and accompanying text). Figure S11 shows the Cr 2p spectra for TiO2G-Au9-CrO<sup>x</sup> before and after heating of the three different concentrations. All the Cr 2p3/2 peak positions are given in Table S4 and the peak positions are discussed in the Supplementary Section.

#### *3.8. Effect of the TiO<sup>2</sup> Film Thickness*

The protective effect of the CrO<sup>x</sup> layer on the agglomeration of Au<sup>9</sup> clusters is not the same for both the TiO2P and TiO2G substrates. The agglomeration of Au<sup>9</sup> clusters is inhibited on TiO2P with the CrO<sup>x</sup> overlayer but not on TiO2G, which shows a higher degree of agglomeration. The coverage of the CrO<sup>x</sup> layer on Au<sup>9</sup> clusters for both substrates is demonstrated by the decrease in the Au-XPS intensities. After heating, it is observed that the relative amount of CrO<sup>x</sup> decreases for both films (Table S5). Our previous studies on a similar system revealed that the CrO<sup>x</sup> layer diffuses into a TiO<sup>2</sup> film after heating to 600 °C due to the differences in surface energy between TiO<sup>2</sup> and CrO<sup>x</sup> [26]. In this study, both films were heated to only 200 °C, however, CrO<sup>x</sup> on TiO2G experienced more diffusion of CrO<sup>x</sup> into the film compared to TiO2P. One possibility for the higher degree of Au<sup>9</sup> agglomeration and CrO<sup>x</sup> diffusion is the mobility of the TiO<sup>2</sup> film. Cluster agglomeration can be due to either (i) growth of the clusters over the surface or (ii) mobility of the substrate. In the case of (i), the cluster growth and agglomeration on a substrate can be ascribed to either Smoluchowski ripening or Ostwald ripening mechanisms. For Smoluchowski ripening, the agglomeration of clusters is caused by the collision and coalescence of entire clusters to larger particles [37]. For Ostwald ripening, the growth of larger particles takes place by the detachment of single atoms, which diffuse onto a nearby cluster or nanoparticle [38]. In the case of (ii), a section of the substrate to which a cluster is adsorbed moves closer to another section of the substrate, which has another adsorbed cluster. The significant change in the surface morphology of TiO2G after heating (Ra: 11.7 nm and Rq: 13.4 nm) compared to TiO2P (Ra: 0.4 nm and Rq: 0.5 nm) strongly suggests that the agglomeration of the Au<sup>9</sup> clusters with different concentrations on TiO2G after heating is due to the high distortion of the surface upon heating. A higher mobility of the TiO<sup>2</sup> substrate during heating means that the local surface beneath an Au cluster moves larger distances compared to a substrate which exhibits lower mobility during heating (see Scheme 2). The high mobility of the thick film is assumed to be due to the recrystallisation during heating, which is in agreement with previous studies [17,19,30]. With increasing mobility, the likelihood of close contact between two or more Au clusters increases, and thus the likelihood of agglomeration is also increased. Furthermore, the degree of agglomeration of the Au clusters is larger for the thicker TiO2G substrate compared to the thinner TiO2P substrate. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 10 of 13 clusters to larger particles [37]. For Ostwald ripening, the growth of larger particles takes place by the detachment of single atoms, which diffuse onto a nearby cluster or nanoparticle [38]. In the case of (ii), a section of the substrate to which a cluster is adsorbed moves closer to another section of the substrate, which has another adsorbed cluster. The significant change in the surface morphology of TiO2G after heating (Ra: 11.7 nm and Rq: 13.4 nm) compared to TiO2P (Ra: 0.4 nm and Rq: 0.5 nm) strongly suggests that the agglomeration of the Au<sup>9</sup> clusters with different concentrations on TiO2G after heating is due to the high distortion of the surface upon heating. A higher mobility of the TiO<sup>2</sup> substrate during heating means that the local surface beneath an Au cluster moves larger distances compared to a substrate which exhibits lower mobility during heating (see Scheme 2). The high mobility of the thick film is assumed to be due to the recrystallisation during heating, which is in agreement with previous studies [17,19,30]. With increasing mobility, the likelihood of close contact between two or more Au clusters increases, and thus the likelihood of agglomeration is also increased. Furthermore, the degree of agglomeration of the Au clusters is larger for the thicker TiO2G substrate compared to the thinner TiO2P substrate.

**Scheme 2.** Schematic illustration showing the agglomeration mechanism of Au<sup>9</sup> clusters on the TiO2G film during heating. **Scheme 2.** Schematic illustration showing the agglomeration mechanism of Au<sup>9</sup> clusters on the TiO2G film during heating.

#### **4. Conclusions**

Au<sup>9</sup> clusters after heating.

**4. Conclusions** In summary, the change in surface morphology of two different film thicknesses of RF sputter-deposited TiO<sup>2</sup> (~400 nm and ~1100 nm) was examined and compared upon heating. After heating, the thick TiO<sup>2</sup> film showed a larger change in surface morphology, which is associated with higher mobility during heating compared to the thin TiO<sup>2</sup> film. In summary, the change in surface morphology of two different film thicknesses of RF sputter-deposited TiO<sup>2</sup> (~400 nm and ~1100 nm) was examined and compared upon heating. After heating, the thick TiO<sup>2</sup> film showed a larger change in surface morphology, which is associated with higher mobility during heating compared to the thin TiO<sup>2</sup> film. The difference in mobility is attributed to the differences in the total amount of amorphous

The difference in mobility is attributed to the differences in the total amount of amorphous TiO<sup>2</sup> transformed to anatase in each of the films, which then results in differences in the

deposition of the CrO<sup>x</sup> layer. After heating, the Au clusters on the thicker film showed a larger degree of agglomeration compared to the thinner film. The higher mobility of the thick film during heating increased the probability of close encounters of Au clusters, which resulted in agglomeration of the Au<sup>9</sup> clusters even in the presence of a CrO<sup>x</sup> overlayer. In contrast, the lower mobility of the thin film resulted in less agglomeration of the

**Supplementary Materials:** The following supporting information can be downloaded at: www.mdpi.com/xxx/s1. The supporting information shows the EDAX-SEM elemental mapping of the TiO2P and TiO2G cross-section images, the details of the XP spectra, their fitting, and quantification. Figure S1: A photo of the TiO2P (lift) and TiO2G (right) films. Figure S2: UV-Vis spectrum of Au9(PPh3)8(NO3)<sup>3</sup> in Methanol. Figure S3: Cross-section SEM-EDAX elemental maps of Ti, O and Si of TiO2P and TiO2G. Note that the scale bars are different. Figure S4: 3D Profile of (A) TiO2P before heating, (B) TiO2P after heating, (C) before heating, TiO2G and (D) TiO2G after heating (area 16 × 16

TiO<sup>2</sup> transformed to anatase in each of the films, which then results in differences in the morphology of the surface upon heating. Au<sup>9</sup> clusters were used as a probe for TiO<sup>2</sup> mobility. Au<sup>9</sup> clusters were deposited onto the two different TiO<sup>2</sup> films, followed by photodeposition of the CrO<sup>x</sup> layer. After heating, the Au clusters on the thicker film showed a larger degree of agglomeration compared to the thinner film. The higher mobility of the thick film during heating increased the probability of close encounters of Au clusters, which resulted in agglomeration of the Au<sup>9</sup> clusters even in the presence of a CrO<sup>x</sup> overlayer. In contrast, the lower mobility of the thin film resulted in less agglomeration of the Au<sup>9</sup> clusters after heating.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/nano12183218/s1. The supporting information shows the EDAX-SEM elemental mapping of the TiO2P and TiO2G cross-section images, the details of the XP spectra, their fitting, and quantification. Figure S1: A photo of the TiO2P (lift) and TiO2G (right) films. Figure S2: UV-Vis spectrum of Au<sup>9</sup> (PPh<sup>3</sup> )8 (NO<sup>3</sup> )3 in Methanol. Figure S3: Cross-section SEM-EDAX elemental maps of Ti, O and Si of TiO2P and TiO2G. Note that the scale bars are different. Figure S4: 3D Profile of (A) TiO2P before heating, (B) TiO2P after heating, (C) before heating, TiO2G and (D) TiO2G after heating (area 16 × 16 µm). Figure S5: Surface morphology with the average of Ra and Rq values of (A) TiO2P before heating, (B) TiO2P after heating, (C) before heating, TiO2G and (D) TiO2G after heating. (area 595 × 595 µm). It is important to know that the scale bars are different. Figure S6: XP spectra of Au 4f of (A) TiO2P-Au<sup>9</sup> : after Au<sup>9</sup> deposition (blue) and after heating (grey) (B) TiO2P-Au<sup>9</sup> -CrOx: after Au<sup>9</sup> deposition (blue), after CrO<sup>x</sup> layer photodeposited (orange) and after heating (grey). Figure S7: XP spectra of Au 4f of (A) TiO2G-Au<sup>9</sup> : after Au<sup>9</sup> deposition (blue) and after heating (grey) (B) TiO2G-Au<sup>9</sup> -CrOx: after Au<sup>9</sup> deposition (blue), after CrO<sup>x</sup> layer photodeposited (orange) and after heating (grey). Figure S8: XP spectra of P 2p of (A) TiO2P-Au<sup>9</sup> : after Au<sup>9</sup> deposition (blue) and after heating (grey) (B) TiO2P-Au<sup>9</sup> -CrOx: after Au<sup>9</sup> deposition (blue), after CrO<sup>x</sup> layer photodeposited (orange), and after heating (grey). Figure S9: XP spectra of Cr 2p of the TiO2P-Au<sup>9</sup> -CrOx sample of (A) 0.006mM sample, (B) 0.06mM sample and (C) 0.6mM sample: after CrO<sup>x</sup> layer photodeposited (orange) and after heating (grey). Figure S10: XP spectra of P 2p of (A) TiO2G-Au<sup>9</sup> : after Au<sup>9</sup> deposition (blue) and after heating (grey) (B) TiO2G-Au<sup>9</sup> -CrOx: after Au<sup>9</sup> deposition (blue), after CrO<sup>x</sup> layer photodeposited (orange), and after heating (grey). Figure S11: XP spectra of Cr 2p of the TiO2G-Au<sup>9</sup> -CrOx sample of (A) 0.006mM sample, (B) 0.06mM sample and (C) 0.6mM sample: after CrO<sup>x</sup> layer photodeposited (orange) and after heating (grey). Table S1: XPS Au 4f7/2 peak positions and FWHM of TiO2P-Au<sup>9</sup> and TiO2P-Au<sup>9</sup> -CrOx. Table S2: XPS Au 4f7/2 peak positions and FWHM of TiO2G-Au<sup>9</sup> and TiO2G-Au<sup>9</sup> -CrOx. Table S3: XPS Cr 2p3/2 peak positions and FWHM of TiO2P-Au<sup>9</sup> -CrOx. Table S4: XPS Cr 2p3/2 peak positions and FWHM of TiO2G-Au<sup>9</sup> -CrOx. Table S5: XPS relative amount of Cr 2p3/2 to Ti 2p3/2 of TiO2P-Au<sup>9</sup> -CrOx and TiO2G-Au<sup>9</sup> -CrOx. References [39–44] are cited in the supplementary materials.

**Author Contributions:** Conceptualization, A.S.A., G.F.M. and G.G.A.; Data curation, A.S.A. and G.G.A.; Formal analysis, A.S.A., Y.Y. and A.R.; Funding acquisition, G.F.M. and G.G.A.; Investigation, A.S.A., Y.Y. and A.R.; Methodology, A.S.A., G.F.M. and G.G.A.; Resources, S.T. and G.G.A.; Supervision, G.G.A.; Visualization, A.S.A.; Writing—original draft, A.S.A.; Writing—review & editing, A.S.A., Y.Y., A.R., S.T., G.F.M. and G.G.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** Australian Synchrotron, Victoria, Australia (AS1/SXR/15819); US Army project FA5209-16- R-0017; Australian Solar Thermal Research Institute (ASTRI), a project supported by the Australian Government, through the Australian Renewable Energy Agency (ARENA).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Acknowledgments:** Part of this research was undertaken on the soft X-ray spectroscopy beamline at the Australian Synchrotron, Victoria, Australia (AS1/SXR/15819). The work was supported by the US Army project FA5209-16-R-0017. This research was performed as part of the Australian Solar Thermal Research Institute (ASTRI), a project supported by the Australian Government, through the Australian Renewable Energy Agency (ARENA). We would like to thank Dr Bruce Cowie from the Australian Synchrotron for his assistance. The authors acknowledge the facilities, and the scientific and technical assistance, of Microscopy Australia (formerly known as AMMRF) and the Australian National Fabrication Facility (ANFF) at Flinders University. The authors acknowledge Flinders Microscopy and Microanalysis and their expertise. The authors thank A/Prof Vladimir Golovko (Canterbury University) for providing access to the Au<sup>9</sup> (PPh<sup>3</sup> )8 (NO<sup>3</sup> )<sup>3</sup> clusters. The authors acknowledge Dr Benjamin Wade at Adelaide Microscopy (University of Adelaide).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Novel InGaSb/AlP Quantum Dots for Non-Volatile Memories**

**Demid S. Abramkin 1,2 and Victor V. Atuchin 3,4,5,6,\***


**Abstract:** Non-volatile memories based on the flash architecture with self-assembled III–V quantum dots (SAQDs) used as a floating gate are one of the prospective directions for universal memories. The central goal of this field is the search for a novel SAQD with hole localization energy (*E*loc) sufficient for a long charge storage (10 years). In the present work, the hole states' energy spectrum in novel InGaSb/AlP SAQDs was analyzed theoretically with a focus on its possible application in nonvolatile memories. Material intermixing and formation of strained SAQDs from a Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* , In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* or an In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* alloy were taken into account. Critical sizes of SAQDs, with respect to the introduction of misfit dislocation as a function of alloy composition, were estimated using the force-balancing model. A variation in SAQDs' composition together with dot sizes allowed us to find that the optimal configuration for the non-volatile memory application is GaSbP/AlP SAQDs with the 0.55–0.65 Sb fraction and a height of 4–4.5 nm, providing the *E*loc value of 1.35–1.50 eV. Additionally, the hole energy spectra in unstrained InSb/AlP and GaSb/AlP SAQDs were calculated. *E*loc values up to 1.65–1.70 eV were predicted, and that makes unstrained InGaSb/AlP SAQDs a prospective object for the non-volatile memory application.

**Keywords:** QD-Flash; self-assembled quantum dots; quantum dots memories; non-volatile memories; universal memories; hole localization; quaternary alloy; strain

#### **1. Introduction**

Semiconductor self-assembled quantum dots (SAQDs) are nanocrystals of a narrow bandgap material grown into a matrix or a shell of a wider bandgap material. In contrast to colloidal SAQDs [1,2], the epitaxial SAQDs formation occurs in Stranski–Krastanov growth mode as a result of surface relief reorganization [3]. One of the crucial advantages of this self-organized growth mode is the formation of a nanoscale objects array without using nanoscale lithography. The flexibility of the SAQD energy spectrum, caused by quantum confinement effects and the alloy composition variation, makes them widely applicable in broad areas of modern electronics and optoelectronics [4–11]. The energy bands offset at an SAQD/matrix heterointerface provide a charge carrier localization into SAQDs, and that opens up the prospective of using SAQDs for charge storage in non-volatile memory cells. The most interesting object in this research field is the construction of a flash memory with a III–V SAQD array used as a floating gate. The basic principles of such memory cells were formulated in [12,13]. The basic idea consists in the hole localization in the SAQD potential that permits controlling the underlying channel conductivity by the field effect, as shown in the schematic diagram presented in Figure 1 [12].

**Citation:** Abramkin, D.S.; Atuchin, V.V. Novel InGaSb/AlP Quantum Dots for Non-Volatile Memories. *Nanomaterials* **2022**, *12*, 3794. https://doi.org/10.3390/ nano12213794

Academic Editor: Orion Ciftja

Received: 22 September 2022 Accepted: 25 October 2022 Published: 27 October 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

[12].

[12].

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 2 of 22

**Figure 1.** (**a**) Schematic cross section of the layered structure. (**b**) Sketch of the SAQD–Flash prototype. Hall-contacts were used for the transport measurements of 2DHG [12]. **Figure 1.** (**a**) Schematic cross section of the layered structure. (**b**) Sketch of the SAQD–Flash prototype. Hall-contacts were used for the transport measurements of 2DHG [12]. The fabrication of the first high-temperature SAQD flash memory prototype, based

The fabrication of the first high-temperature SAQD flash memory prototype, based on InAs/AlGaAs SAQDs [13,14], reveals the main advantages of III–V SAQD flash cells in comparison with traditional Si/SiO2-based ones. First of all, a significantly faster access time (about 20 ns) was mentioned [13], and that is comparable to a dynamic random-access memory (DRAM), in contrast to microsecond times common for a Si/SiO2-based flash memory in the framework of planar technology. As is clearly seen in Figure 2 [12], the fast access is caused by (i) the direct hole capture into an SAQD at the writing mode with the rate limited by the hole energy relaxation and recharging of the structure capacitance (*f*cutoff ~ 1/(*RC)*) only and (ii) the tunnel hole emission at the erase mode [13,15]. Miniaturization of the cell III–V of the SAQD-memory will minimize the limitation of the write/erase rate caused by recharging the capacitance of the structure and allow it to approach the limit determined by the hole capture time in the SAQD (less than 1 ps [16]). Second, in traditional Si/SiO2-based flash memories, hot charge-carriers are used for the write/erase procedure, and it leads to a damaging of the structure and low endurance (<106 cycles). The direct hole capture into SAQDs, according to the SAQD flash concept, will solve this problem and allow a significant increase in endurance. Additionally, the advantage of using III–V materials is that III–V FETs are noticeably superior to Si FETs in their speed characteristics [17]. This allows us to hope for an increase in the speed of reading data from the memory cells due to the higher mobility of charge carriers in the transistor channel. In addition, the similarity of the structure of materials III–V and Si, as well as close values of technological norms of lithography and other post-growth processes for Si and III–V chips [18], suggest that: (i) the planar cell density of III–V SAQD-memory can reach that of planar Si flash and DRAM, and (ii) III–V flash technology can walk the path that Si flash technology has traveled and take full advantage of the 3D memory architecture. All these SAQD flash memory features are a perspective for the creation of universal memory, which combines the advantages of a fast DRAM memory and a long storage time of a non-volatile flash memory, and that allows for expecting a revolution in computer architecture. It is also necessary to note that some of the III–V materials are characterized by a high probability of optical interband transitions. This allows us to hope for the development of memory with optical The fabrication of the first high-temperature SAQD flash memory prototype, based on InAs/AlGaAs SAQDs [13,14], reveals the main advantages of III–V SAQD flash cells in comparison with traditional Si/SiO2-based ones. First of all, a significantly faster access time (about 20 ns) was mentioned [13], and that is comparable to a dynamic random-access memory (DRAM), in contrast to microsecond times common for a Si/SiO2-based flash memory in the framework of planar technology. As is clearly seen in Figure 2 [12], the fast access is caused by (i) the direct hole capture into an SAQD at the writing mode with the rate limited by the hole energy relaxation and recharging of the structure capacitance (*f* cutoff ~ 1/(*RC)*) only and (ii) the tunnel hole emission at the erase mode [13,15]. Miniaturization of the cell III–V of the SAQD-memory will minimize the limitation of the write/erase rate caused by recharging the capacitance of the structure and allow it to approach the limit determined by the hole capture time in the SAQD (less than 1 ps [16]). Second, in traditional Si/SiO2-based flash memories, hot charge-carriers are used for the write/erase procedure, and it leads to a damaging of the structure and low endurance (<10<sup>6</sup> cycles). The direct hole capture into SAQDs, according to the SAQD flash concept, will solve this problem and allow a significant increase in endurance. Additionally, the advantage of using III–V materials is that III–V FETs are noticeably superior to Si FETs in their speed characteristics [17]. This allows us to hope for an increase in the speed of reading data from the memory cells due to the higher mobility of charge carriers in the transistor channel. In addition, the similarity of the structure of materials III–V and Si, as well as close values of technological norms of lithography and other post-growth processes for Si and III–V chips [18], suggest that: (i) the planar cell density of III–V SAQD-memory can reach that of planar Si flash and DRAM, and (ii) III–V flash technology can walk the path that Si flash technology has traveled and take full advantage of the 3D memory architecture. All these SAQD flash memory features are a perspective for the creation of universal memory, which combines the advantages of a fast DRAM memory and a long storage time of a non-volatile flash memory, and that allows for expecting a revolution in computer architecture. It is also necessary to note that some of the III–V materials are characterized by a high probability of optical interband transitions. This allows us to hope for the development of memory with optical access, which will accelerate the transition to computing systems based on the principles of photonics. on InAs/AlGaAs SAQDs [13,14], reveals the main advantages of III–V SAQD flash cells in comparison with traditional Si/SiO2-based ones. First of all, a significantly faster access time (about 20 ns) was mentioned [13], and that is comparable to a dynamic random-access memory (DRAM), in contrast to microsecond times common for a Si/SiO2-based flash memory in the framework of planar technology. As is clearly seen in Figure 2 [12], the fast access is caused by (i) the direct hole capture into an SAQD at the writing mode with the rate limited by the hole energy relaxation and recharging of the structure capacitance (*f*cutoff ~ 1/(*RC)*) only and (ii) the tunnel hole emission at the erase mode [13,15]. Miniaturization of the cell III–V of the SAQD-memory will minimize the limitation of the write/erase rate caused by recharging the capacitance of the structure and allow it to approach the limit determined by the hole capture time in the SAQD (less than 1 ps [16]). Second, in traditional Si/SiO2-based flash memories, hot charge-carriers are used for the write/erase procedure, and it leads to a damaging of the structure and low endurance (<106 cycles). The direct hole capture into SAQDs, according to the SAQD flash concept, will solve this problem and allow a significant increase in endurance. Additionally, the advantage of using III–V materials is that III–V FETs are noticeably superior to Si FETs in their speed characteristics [17]. This allows us to hope for an increase in the speed of reading data from the memory cells due to the higher mobility of charge carriers in the transistor channel. In addition, the similarity of the structure of materials III–V and Si, as well as close values of technological norms of lithography and other post-growth processes for Si and III–V chips [18], suggest that: (i) the planar cell density of III–V SAQD-memory can reach that of planar Si flash and DRAM, and (ii) III–V flash technology can walk the path that Si flash technology has traveled and take full advantage of the 3D memory architecture. All these SAQD flash memory features are a perspective for the creation of universal memory, which combines the advantages of a fast DRAM memory and a long storage time of a non-volatile flash memory, and that allows for expecting a revolution in computer architecture. It is also necessary to note that some of the III–V materials are characterized by a high probability of optical interband transitions. This allows us to hope for the development of memory with optical access, which will accelerate the transition to computing systems based on the principles of photonics.

**Figure 2.** Schematic illustration of the (**a**) storage, (**b**) write and (**c**) erase operations in the SAQD–Flash concept [12].

access, which will accelerate the transition to computing systems based on the principles

Nevertheless, developing an SAQD-based non-volatile memory is still far from being finished. The main problem arising in this way is the insufficient hole localization energy

in known SAQDs (*E*loc) resulting in a low charge storage time. Actually, the first hightemperature prototype based on InAs/AlGaAs SAQDs [13,14] was characterized by a storage time of about few milliseconds, caused by *E*loc lower than 0.8 eV. Thus, it became clear that the main weak point of this technology is the insufficient hole localization energy in presently available III–V SAQDs. Further investigations were focused on the SAQD formation in III–V heterosystems with a higher *E*loc value. This trend has involved such well-known SAQDs system as GaSb/GaAs [19–21] and relatively novel heterosystems, for instance, GaSb/AlGaAs [22,23], GaSb/AlAs [24], InSb/AlAs [25], InGaAs/GaP [26,27], GaSb/GaP [28,29], InGaSb/GaP [30,31] and others, as discussed in [32]. The highest *E*loc value was obtained for GaSbP/GaP SAQDs (about 1.18 eV [29]), and it results in a storage time of about four days. As is mentioned in Ref. [32], a storage time longer than 10 years may be reached at *E*loc > 1.3–1.5 eV.

Despite the impressively long charge storage in GaSbP/GaP SAQDs, this is not yet sufficient for a non-volatile memory cell. As it appears, a further increase in *E*loc can be realized by increasing SAQD sizes and/or by the increase in the Sb content in ternary alloy GaSbP. However, it inevitably leads to a rise in strain level and a risk of plastic SAQD relaxation. On the other hand, it is possible to increase the hole localization by downshifting the matrix valence band top using AlP instead of GaP. Indeed, the valence band top in AlP lies ~0.5 eV lower than the GaP valence band top [33]. According to the simplest estimations, this allows us to expect an increase in the localization energy by the same 0.5 eV. According to calculations [12,13,32], an increase in the localization energy by 50 meV provides an increase in the charge storage time at room temperature by one order of magnitude. That is, *ceteris paribus*, replacing the matrix material from GaP to AlP can increase the storage time by 10 orders of magnitude, which corresponds to 10<sup>8</sup> years. However, despite such optimistic forecasts, the InGaSb/AlP heterosystem remains unexplored either theoretically or experimentally. Earlier, the Sb-based SAQDs in the AlP matrix were just briefly mentioned in [29,32,34], and no detailed SAQD energy spectrum calculations and, especially, attempts of epitaxial growth can be found in the literature. Embedding AlGaP barriers in the heterostructures with InGaSb/GaP SAQDs [31] and AlP barriers growing close to InGaAs/GaP SAQDs [27] were only discussed.

In this contribution, we report on the InGaSb/AlP SAQDs' energy spectrum calculations, taking into account the material intermixing and SAQD formation from the alloy with Al and P atoms. It is shown that strained GaSbP/AlP SAQDs are optimal for the non-volatile memory fabrication and allow for expecting the hole localization energy (up to 2.04 eV) along with the minimal elastic strain. Additionally, the unstrained InGaSb/AlP SAQD hole energy spectrum was investigated. The hole localization energy values are predicted up to *E*loc = 1.65–1.70 eV, and it precipitates the prospects of using unstrained InGaSb/AlP SAQDs for non-volatile memory applications.

#### **2. Calculation Procedure**

As was mentioned, a significant variation in the SAQD energy spectrum, provided by a strong influence of SAQD geometry and alloy composition on the energy level position, is the key feature inducing the technological interest in SAQD heterostructures. On the other hand, the energy spectrum's sensitivity to SAQD parameters makes the spectrum prediction a complicated task, requiring a wide range of parameters' variation. The present work is aimed at the theoretical investigation of the energy spectrum for novel InGaSb/AlP SAQDs depending on SAQD sizes and the alloy composition with the focus on hole localization energy.

First, we need to discuss the SAQD shape, which was used for modeling. Here, it is necessary to observe the available experimental data related to the III–V SAQD formation. InAs/GaAs is the most investigated III–V heterosystem. There is a huge quantity of experimental data indicating that, for the InAs/GaAs SAQDs, the nanostructures of different shapes, including disks, truncated cones, lenses, pyramids or truncated pyramids, can be produced by Stranski–Krastanov growth techniques [6,35–40]. Comparatively, SAQDs

formed in the III-phosphide matrixes were rarely studied. The experimental data related to InGaAs/GaP [26], GaSb/GaP [41] and InGaSb/GaP [30] SAQDs allow us to use the truncated pyramid shape for modeling InGaSb/AlP SAQDs. Following [41], where the dot shapes were discussed in detail, we select a pyramid with a square base oriented along [011]-like directions and limited by lateral (111) and top (100) facets with the SAQD aspect ratio of 1:4. The SAQD shape used for modeling is shown in Figure 3. mental data related to InGaAs/GaP [26], GaSb/GaP [41] and InGaSb/GaP [30] SAQDs allow us to use the truncated pyramid shape for modeling InGaSb/AlP SAQDs. Following [41], where the dot shapes were discussed in detail, we select a pyramid with a square base oriented along [011]-like directions and limited by lateral (111) and top (100) facets with the SAQD aspect ratio of 1:4. The SAQD shape used for modeling is shown in Figure 3.

First, we need to discuss the SAQD shape, which was used for modeling. Here, it is necessary to observe the available experimental data related to the III–V SAQD formation. InAs/GaAs is the most investigated III–V heterosystem. There is a huge quantity of experimental data indicating that, for the InAs/GaAs SAQDs, the nanostructures of different shapes, including disks, truncated cones, lenses, pyramids or truncated pyramids, can be produced by Stranski–Krastanov growth techniques [6,35–40]. Comparatively, SAQDs formed in the III-phosphide matrixes were rarely studied. The experi-

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 4 of 22

**Figure 3.** SAQD shape with the quadratic base along [011]-like directions and limited by (100) top/base planes and (111)-like side planes. **Figure 3.** SAQD shape with the quadratic base along [011]-like directions and limited by (100) top/base planes and (111)-like side planes.

Besides the shape factor, the SAQD energy spectrum may be affected by elastic deformation. All III-phosphides and III-antimonides are of the same crystal structure (zinc blend) type, but the crystals are characterized by quite different lattice constants. In the most strained case of the InSb/AlP pair, the difference is as high as 15% [33]. Therefore, the nanoislands are inevitably formed with elastic strains. According to the model-solid theory [42], a strain leads to an energy band shift that, consequently, has its effect on the SAQD energy spectrum. Unfortunately, when the elastic energy of SAQD exceeds some critical level, plastic relaxation processes can occur and threading dislocations can be generated [43–46]. A distortion of translation symmetry in the dislocation core results in the appearance of deep centers close to the SAQDs, and it could lead to the tunnel hole escape from an SAQD and, consequently, to a dramatic shortening of hole storage time. Moreover, threading dislocations provide an electric bypass in the heterostructure that hinders the band-bending control by the gate bias. Thus, the calculation of critical SAQD sizes, accounting for the effects related to the introduction of dislocations, is an important Besides the shape factor, the SAQD energy spectrum may be affected by elastic deformation. All III-phosphides and III-antimonides are of the same crystal structure (zinc blend) type, but the crystals are characterized by quite different lattice constants. In the most strained case of the InSb/AlP pair, the difference is as high as 15% [33]. Therefore, the nanoislands are inevitably formed with elastic strains. According to the model-solid theory [42], a strain leads to an energy band shift that, consequently, has its effect on the SAQD energy spectrum. Unfortunately, when the elastic energy of SAQD exceeds some critical level, plastic relaxation processes can occur and threading dislocations can be generated [43–46]. A distortion of translation symmetry in the dislocation core results in the appearance of deep centers close to the SAQDs, and it could lead to the tunnel hole escape from an SAQD and, consequently, to a dramatic shortening of hole storage time. Moreover, threading dislocations provide an electric bypass in the heterostructure that hinders the band-bending control by the gate bias. Thus, the calculation of critical SAQD sizes, accounting for the effects related to the introduction of dislocations, is an important task in our modeling.

task in our modeling. Furthermore, material intermixing and SAQDs formation from the solid alloy result in the change in basic material parameters, such as lattice constant, bandgap and valence band offset [33], that also influence the strain value and energy band positions. The In*x*Ga1−*x*Sb deposition on AlP can, in general, result in the In*x*Ga1−*x*Sb*y*P1−*y*/AlP SAQDs formation. The material intermixing can occur during the III-Sb deposition stage due to bulk interdiffusion [47–50], as well as during the growth of cap AlP layers due to the material segregation and exchange reaction between the SAQD and the AlP matrix [51– 59]. In order to simplify calculations, we considered SAQDs consisting of quaternary alloys Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y*. As is shown below, this simplification does not decrease the interest in our results, but allows us to demonstrate the main regularity of the SAQD energy spectrum depending on the alloy composition. Thus, the calculation procedure can be subdivided into the following stages: (i) calculation of critical SAQD size depending on the SAQD alloy composition, (ii) taking into account the effect of material mixing on the SAQD material parameters, (iii) calculations of strain Furthermore, material intermixing and SAQDs formation from the solid alloy result in the change in basic material parameters, such as lattice constant, bandgap and valence band offset [33], that also influence the strain value and energy band positions. The In*x*Ga1−*x*Sb deposition on AlP can, in general, result in the In*x*Ga1−*x*Sb*y*P1−*y*/AlP SAQDs formation. The material intermixing can occur during the III-Sb deposition stage due to bulk interdiffusion [47–50], as well as during the growth of cap AlP layers due to the material segregation and exchange reaction between the SAQD and the AlP matrix [51–59]. In order to simplify calculations, we considered SAQDs consisting of quaternary alloys Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*y*. As is shown below, this simplification does not decrease the interest in our results, but allows us to demonstrate the main regularity of the SAQD energy spectrum depending on the alloy composition. Thus, the calculation procedure can be subdivided into the following stages: (i) calculation of critical SAQD size depending on the SAQD alloy composition, (ii) taking into account the effect of material mixing on the SAQD material parameters, (iii) calculations of strain distribution in SAQDs, (iv) SAQD band alignment calculations and (v) charge carrier energy level calculations. Let us describe this algorithm in detail.

#### *2.1. Critical Sizes Calculation*

The introduction of the dislocation occurs when the critical SAQD elastic energy level is reached [43–46], and it is governed by SAQD sizes and SAQD/matrix lattice constant mismatch *f* dependent on the SAQD alloy composition. Thus, we need to calculate the critical sizes of SAQD as a function of the alloy composition. The force-balance approach [60,61]

was used for the critical SAQD sizes calculation. This approach was developed by Fischer for the prediction of critical thickness when the dislocations are introduced in strained films, and, also, it was successfully used for the critical thickness prediction in the GeSi/Si layers [61]. For the III–V SAQD, the approach was first used in [60]. In the framework of this approach, the equilibrium situation is provided by the competition of two forces: (i) strainassisted force that leads to the dislocation introduction and (ii) dislocation loop tension directed to the minimization of the total dislocation length. To simplify the calculations, in our case, the problem was simplified to the interaction between two 90◦ Lomer dislocations. Indeed, as is presented by the SAQD sketch given in Figure 4 [60], 60◦ dislocations in the SAQD can join and form 90◦ Lomer dislocations. These Lomer dislocations, lying at the bottom and top SAQD heterointerfaces, form the dislocation dipole (i.e., dislocations with equal, but opposite Burgers vectors). proach [60,61] was used for the critical SAQD sizes calculation. This approach was developed by Fischer for the prediction of critical thickness when the dislocations are introduced in strained films, and, also, it was successfully used for the critical thickness prediction in the GeSi/Si layers [61]. For the III–V SAQD, the approach was first used in [60]. In the framework of this approach, the equilibrium situation is provided by the competition of two forces: (i) strain-assisted force that leads to the dislocation introduction and (ii) dislocation loop tension directed to the minimization of the total dislocation length. To simplify the calculations, in our case, the problem was simplified to the interaction between two 90° Lomer dislocations. Indeed, as is presented by the SAQD sketch given in Figure 4 [60], 60° dislocations in the SAQD can join and form 90° Lomer dislocations. These Lomer dislocations, lying at the bottom and top SAQD heterointerfaces, form the dislocation dipole (i.e., dislocations with equal, but opposite Burgers vectors).

distribution in SAQDs, (iv) SAQD band alignment calculations and (v) charge carrier

The introduction of the dislocation occurs when the critical SAQD elastic energy level is reached [43–46], and it is governed by SAQD sizes and SAQD/matrix lattice constant mismatch *f* dependent on the SAQD alloy composition. Thus, we need to calculate the critical sizes of SAQD as a function of the alloy composition. The force-balance ap-

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 5 of 22

energy level calculations. Let us describe this algorithm in detail.

*2.1. Critical Sizes Calculation* 

**Figure 4.** Location of dislocation loops around the SAQD; 60° dislocations tend to combine into Lomer dislocations (L). A dislocation loop (left) fails to wrap around the dot and threads towards the surface [60]. **Figure 4.** Location of dislocation loops around the SAQD; 60◦ dislocations tend to combine intoLomer dislocations (L). A dislocation loop (left) fails to wrap around the dot and threads towards the surface [60].

A distance between dislocations in a dipole corresponding to a dot height can be obtained from the equilibrium condition on the forces acting on dislocation loops, and it leads to the absence of excess shear stress *τ*exc: A distance between dislocations in a dipole corresponding to a dot height can beobtained from the equilibrium condition on the forces acting on dislocation loops, and itleads to the absence of excess shear stress *<sup>τ</sup>*exc:

$$\tau\_{\rm exc} = \cos \lambda \cos \rho \,\,\frac{2G(1+\nu)}{1-\nu} \left( f - \frac{b \cos \lambda}{2R\_{h,p}} (1+\beta) \right) = 0 \tag{1}$$

with with

$$\beta = \frac{1 - \frac{\nu}{4}}{4\pi \cos^2 \lambda} \ln\left(\frac{\mathcal{R}\_{h,p}}{b}\right) \tag{2}$$

$$R\_{h,p} = \left(\frac{4}{h^2} + \frac{4}{p^2}\right)^{-\frac{1}{2}}\tag{3}$$
 
$$\text{en the Burgers vector and the direction in the interface}$$

2 2 *h p Rh,p* (3) where *λ* = 60° is the angle between the Burgers vector and the direction in the interface plane that is normal to the dislocation line, *φ* = 35.3° is the angle between the slip plane and the strained interface normal, *G* is the shear modulus, ν *=* 0.31 is the Poisson ratio (close for all binary antimonides and phosphides), *f* is the lattice mismatch between an where *λ* = 60◦ is the angle between the Burgers vector and the direction in the interface plane that is normal to the dislocation line, *ϕ* = 35.3◦ is the angle between the slip plane and the strained interface normal, *G* is the shear modulus, *ν =* 0.31 is the Poisson ratio (close for all binary antimonides and phosphides), *f* is the lattice mismatch between an SAQD alloy and AlP matrix, *b =*a/<sup>√</sup> 2 is the Burgers vector magnitude (*a* is the SAQD lattice constant), *h* is the separation between two segments of the dislocation dipole and *p* is the lateral separation between two dislocations. Since the introduction of one dislocation was considered, the *p* value was increased to the infinity. Solving this transcendent equation by the graphical method (see sample plot in Figure S1 in the Supplementary Materials) and varying *f* and *b* according to the alloy composition by the linear Vegard law for quaternary alloys of generalized composition *AxB*1−*xCyD*1−*<sup>y</sup>* ( *aABCD* = *xy* · *aAC* + (1 − *x*) *y* · *aBC* + (1 − *x*)(1 − *y*) · *aBD* + *x*(1 − *y*) · *aAD*), we obtained the critical SAQD height (*h*c) as a function of alloy composition. The obtained *h*<sup>c</sup> values were used for consequent calculations.

#### *2.2. Effect of Alloy Composition*

The formation of a solid alloy from different atom species results in a disorder and material parameter fluctuation on a micro scale, comparable with few interatomic distances [62–65]. However, typical SAQD sizes of several nanometers [3–11] significantly exceed this distance, and this fact allows us to neglect the disorder and consider a solid alloy as a material with averaged constant parameters governed by the alloy composition. Material parameters for quaternary alloys of the *AxB*1−*xCyD*1−*<sup>y</sup>* type were calculated in the quadratic approach using expression [33]:

$$\begin{array}{c} \text{P}\_{\text{ABCD}} = \text{xy} \cdot \text{P}\_{\text{AC}} + (1 - \text{x})y \cdot \text{P}\_{\text{BC}} + (1 - \text{x})(1 - y) \cdot \text{P}\_{\text{BD}} + \text{x}(1 - y) \cdot \text{P}\_{\text{AD}} + \\ + \text{x}(1 - \text{x})y \cdot \text{C}\_{\text{ABC}} + (1 - \text{x})y(1 - y) \cdot \text{C}\_{\text{BCD}} + \text{x}(1 - \text{x})(1 - y) \cdot \text{C}\_{\text{ABD}} + \text{xy}(1 - y) \cdot \text{C}\_{\text{ACD}} \end{array} \tag{4}$$

where *x* and *y* are the fractions of corresponding atoms, *P*ij is the parameter value for binary compounds and *C*ijk is the bowing parameters for the corresponding ternary alloys.

During the SAQD formation, material intermixing processes may result in the distribution of alloy composition over the SAQD bulk. The studies of composition variation in the well-known ternary alloy In*x*Ga1−*x*As/GaAs SAQDs yielded a reverse triangle distribution of the In content along the growth axis [35,36], where the In content rises to the SAQD top. However, quaternary and more complicated alloy SAQDs have not been investigated in such detail. In one of few contributions related to the consideration of multielement alloy SAQDs, the experimental data were reported for the atom distributions in InGaAsSb/GaP SAQDs grown on the GaAs sublayer [66]. The non-uniform element distributions along the growth direction were determined. The trends of element distribution were close to the triangle shapes, but the peak positions for In and Sb were shifted to the SAQD top in reference to the peak positions for Ga, P and As, and that was caused by drastically different segregation effects. However, the available data are not essential to see how the element profiles are changed as a function of average element content. Therefore, in order to simplify the calculation procedure, we used the SAQD model with a fixed alloy composition over the SAQD bulk. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 7 of 22 *<sup>f</sup> <sup>a</sup> a a a a mat || xx yy* <sup>=</sup> <sup>−</sup> <sup>=</sup> <sup>−</sup> <sup>=</sup> <sup>=</sup> <sup>1</sup> 0 0 0 ε ε (6) where *a*<sup>0</sup> is the unstrained lattice constant of thin layer material. According to the model-solid approach, the in-plane deformation induces the corresponding deformation

#### *2.3. Strain Distribution*

[71].

*2.4. Band Alignment Calculation* 

Since the typical SAQD size drastically exceeds the interplanar distances in III–V materials, the SAQD material can be considered as a continuous matter. The strain was calculated in the framework of the model-solid approach [42]. A thin 2D layer coherently strained to the surrounding matrix and arranged along the (100) plane is schematically presented in Figure 5. Both layer and matrix materials are related to the zinc blend type. The lateral lattice constant of the thin layer is equal to the lattice constant of the unstrained matrix: <sup>=</sup> <sup>−</sup> <sup>⊥</sup> *xx <sup>C</sup> <sup>C</sup> <sup>a</sup> <sup>a</sup>* ε 11 12 <sup>0</sup> 1 2 (7) where *C*12 and *C*11 are the elastic constants of a thin layer material. Thus, the component of the deformation tensor along the growth axis is: *<sup>f</sup> <sup>C</sup> C a* 12 = −1 = −2 <sup>⊥</sup> ε(8)

along the growth axis. The lattice constant of the thin layer in the growth axis direction is:

*a*

*zz*

*a*


, that controls the change in the unit

, that accounts for the distortion of the unit cell

**Figure 5.** Thin layer of the material with a high lattice constant coherently strained to the matrix of a material with a low lattice constant. **Figure 5.** Thin layer of the material with a high lattice constant coherently strained to the matrix of a material with a low lattice constant.

In this simple case, the deformation is almost localized in the thin strained layer, in contrast to the case of 3D SAQD, where the surrounding matrix layers are also strained [67–70]. The strain distribution over the SAQD volume and attached matrix material was calculated by the elastic energy minimization technique. This technique is based on the

The SAQD band alignment was calculated in two steps [42]. First, the band alignment for an unstrained SAQD was obtained using the valence band offsets (VBO) and bandgap energy values for the solid alloy [33]. Then, the band edge shift due to the elastic strain was taken into account using deformation potentials [42]. The strain itself can be

> ε +ε + ε

shape. A hydrostatic strain leads to a change in charge density in a crystal, and that has the effect on bandgaps. The biaxial strain results in the reduction in the unit cell symmetry, and it affects the degenerated energy bands' splitting in *X* electron valleys and heavy-, light- and spin-orbital splitting hole sub-bands at the *Г* point of the Brillouin zone for the zinc blend type crystals. Note that *L* electron valleys are not subject to splitting in the case of the (100) oriented interface. The band edge shifting due to hydrostatic strain *H* 

ε −ε

divided into the hydrostatic strain *H xx yy zz* =

can be calculated by the following simple expression:

cell volume, and biaxial strain *zz xx I* =

Therefore, the lateral component of deformation tensor *εxx* can be written as:

$$
\varepsilon\_{\rm xx} = \varepsilon\_{yy} = \frac{a\_{||} - a\_0}{a\_0} = \frac{a\_{\rm mat}}{a\_0} - 1 = f \tag{6}
$$

where *a*<sup>0</sup> is the unstrained lattice constant of thin layer material. According to the modelsolid approach, the in-plane deformation induces the corresponding deformation along the growth axis. The lattice constant of the thin layer in the growth axis direction is:

$$a\_{\perp} = a\_0 \left( 1 - 2 \frac{\mathcal{C}\_{12}}{\mathcal{C}\_{11}} \varepsilon\_{\text{xx}} \right) \tag{7}$$

where *C*<sup>12</sup> and *C*<sup>11</sup> are the elastic constants of a thin layer material. Thus, the component of the deformation tensor along the growth axis is:

$$
\varepsilon\_{zz} = \frac{a\_\perp}{a\_0} - 1 = -2\frac{\mathbf{C}\_{12}}{\mathbf{C}\_{11}}f \tag{8}
$$

In this simple case, the deformation is almost localized in the thin strained layer, in contrast to the case of 3D SAQD, where the surrounding matrix layers are also strained [67–70]. The strain distribution over the SAQD volume and attached matrix material was calculated by the elastic energy minimization technique. This technique is based on the mesh point positions' variation until the total elastic energy of the system reaches a minimum. The calculations were performed using the Nextnano++ program package [71].

#### *2.4. Band Alignment Calculation*

The SAQD band alignment was calculated in two steps [42]. First, the band alignment for an unstrained SAQD was obtained using the valence band offsets (VBO) and bandgap energy values for the solid alloy [33]. Then, the band edge shift due to the elastic strain was taken into account using deformation potentials [42]. The strain itself can be divided into the hydrostatic strain *H* = *εxx* + *εyy* + *εzz*, that controls the change in the unit cell volume, and biaxial strain *I* = *εzz* − *εxx*, that accounts for the distortion of the unit cell shape. A hydrostatic strain leads to a change in charge density in a crystal, and that has the effect on bandgaps. The biaxial strain results in the reduction in the unit cell symmetry, and it affects the degenerated energy bands' splitting in *X* electron valleys and heavy-, light- and spin-orbital splitting hole sub-bands at the point of the Brillouin zone for the zinc blend type crystals. Note that *L* electron valleys are not subject to splitting in the case of the (100) oriented interface. The band edge shifting due to hydrostatic strain *H* can be calculated by the following simple expression:

$$
\Delta E\_i^H = a\_i \ H \tag{9}
$$

where index *i* means the electron , *X* or *L* valley, or valence band and *a*<sup>i</sup> , is the corresponding hydrostatic deformation potential. The *X* electron band edge splits into *X<sup>Z</sup>* sub-bands, where the electron quasi-momentum is orthogonal to the interface, and *XXY* sub-band, where the electron quasi-momentum is parallel to the interface plane. The corresponding energy shifts were determined by expressions:

$$
\Delta E\_Z = \frac{2}{3} b\_X \ I \tag{10}
$$

$$
\Delta E\_{XY} = -\frac{1}{3} b\_X \ I \tag{11}
$$

where *b<sup>X</sup>* is the shear deformation potential for the *X* electron valley. Note that, for the typical case of a narrow bandgap material layer with high lattice constant embedded into a wide bandgap material matrix with low lattice constant, the value of biaxial strain *I* is positive. In combination with the positive values of *b<sup>X</sup>* for all III–V materials (see *Section 2.6* *Materials Parameters* and *Supplementary Materials*), this fact makes ∆*E*<sup>Z</sup> positive and ∆*EXY* negative. The energy splitting for hole subbands is described by relations: a wide bandgap material matrix with low lattice constant, the value of biaxial strain *I* is positive. In combination with the positive values of *bX* for all III–V materials (see section *2.6. Materials Parameters* and *Supplementary Materials*), this fact makes Δ*E*Z positive and

where *bX* is the shear deformation potential for the *X* electron valley. Note that, for the typical case of a narrow bandgap material layer with high lattice constant embedded into

where index *i* means the electron *Г*, *X* or *L* valley, or valence band and *a*i, is the corresponding hydrostatic deformation potential. The *X* electron band edge splits into *XZ* sub-bands, where the electron quasi-momentum is orthogonal to the interface, and *XXY* sub-band, where the electron quasi-momentum is parallel to the interface plane. The

*<sup>E</sup> <sup>b</sup> <sup>I</sup> <sup>Z</sup> <sup>X</sup>* <sup>3</sup>

*<sup>E</sup> <sup>b</sup> <sup>I</sup> XY <sup>X</sup>* <sup>3</sup>

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 8 of 22

corresponding energy shifts were determined by expressions:

$$
\Delta E\_{lh} = -\frac{1}{6}\Delta\_0 + \frac{1}{4}\delta E\_{001} + \frac{1}{2}\left(\Delta\_0^2 + \Delta\_0\delta E\_{001} + \frac{9}{4}\left(\delta E\_{001}\right)^2\right)^{\frac{1}{2}}\tag{12}
$$

$$
\Delta E\_{\rm hh} = \frac{1}{3} \Delta\_0 - \frac{1}{2} \delta E\_{001} \tag{13}
$$

*E ai H <sup>H</sup>* Δ *<sup>i</sup>* = (9)

<sup>2</sup> <sup>Δ</sup> <sup>=</sup> (10)

<sup>1</sup> <sup>Δ</sup> <sup>=</sup> <sup>−</sup> (11)

$$
\Delta E\_{SO} = -\frac{1}{6}\Delta\_0 + \frac{1}{4}\delta E\_{001} - \frac{1}{2}\left(\Delta\_0^2 + \Delta\_0\delta E\_{001} + \frac{9}{4}(\delta E\_{001})^2\right)^{\frac{1}{2}}\tag{14}
$$

where *δE*<sup>001</sup> = 2*bvI*, with valence band shear deformation potential *b<sup>v</sup>* and ∆0—spin-orbit splitting. Note that, in these expressions, energy shifts were calculated in relation to the averaged valence band energy, which lies ∆0/3 lower than the valence band top of an unstrained zinc blende crystal. For clarity, in order to illustrate the band alignment formation for a strained thin layer, we present all the above-described stages in Figure 6 by the example of GaSb/AlP. The band diagram for the unstrained heterojunction is presented in Figure 6a. The energy shifts due to the hydrostatic strain are accounted for in Figure 6b. As is clearly seen from the figure, the hydrostatic strain leads to the shifts in electron and hole band edges without splitting. The total effect of the hydrostatic and biaxial strains on the band alignment is shown in Figure 6c. The biaxial strain leads to energy band splitting, as it is governed by Expressions (10) and (11). where *δE*001 = 2*bvI*, with valence band shear deformation potential *bv* and *Δ*0—spin-orbit splitting. Note that, in these expressions, energy shifts were calculated in relation to the averaged valence band energy, which lies *Δ*0/3 lower than the valence band top of an unstrained zinc blende crystal. For clarity, in order to illustrate the band alignment formation for a strained thin layer, we present all the above-described stages in Figure 6 by the example of GaSb/AlP. The band diagram for the unstrained heterojunction is presented in Figure 6a. The energy shifts due to the hydrostatic strain are accounted for in Figure 6b. As is clearly seen from the figure, the hydrostatic strain leads to the shifts in electron and hole band edges without splitting. The total effect of the hydrostatic and biaxial strains on the band alignment is shown in Figure 6c. The biaxial strain leads to energy band splitting, as it is governed by Expressions (10) and (11).

**Figure 6.** Band alignment for the thin GaSb layer coherently strained to the AlP matrix oriented along the (100) plane. The calculation is performed for 300 K. The band alignment for the un-**Figure 6.** Band alignment for the thin GaSb layer coherently strained to the AlP matrix oriented along the (100) plane. The calculation is performed for 300 K. The band alignment for the unstrained GaSb/AlP layer (**a**), energy shifts due to the hydrostatic strain (**b**) and the both of the hydrostatic and the biaxial strains (**c**) are presented.

#### *2.5. Energy Levels*

The crucial feature of SAQDs, that distinguishes them from other low-dimensional semiconductor heterostructures such as quantum wells or quantum wires, is the 3D chargecarrier localization due to small SAQD sizes, which is comparable with the de Broglie wavelengths of electrons and holes. In order to calculate the charge carrier energy levels in an SAQD, we need to solve the 3D Schrödinger equation for a potential well formed by the SAQD band alignment. The simplest way is a calculation in the simple band approach, when charge carriers are considered as quasi-particles and where the effective mass and the interband interaction is not accounted. However, the interband interaction might result in a shift of energy levels, and it may be significant. The interaction between electrons and heavy-, light- and spin-splitting holes can be taken into account in the framework of the 8-band *k* × *p* approach [72]. We perform the test calculation of energy levels in the unstrained GaSb/AlP SAQD for different sizes using simple band and 8-band *k* × *p* approaches for comparison. The obtained results are shown in Figure 7. The

calculations were performed using the Nextnano++ program package. This program package is commonly used for III–V SAQD energy spectrum calculations [25,28,73,74]. The calculations were performed using the Nextnano++ program package. This program package is commonly used for III–V SAQD energy spectrum calculations [25,28,73,74].

strained GaSb/AlP layer (**a**), energy shifts due to the hydrostatic strain (**b**) and the both of the hy-

The crucial feature of SAQDs, that distinguishes them from other low-dimensional semiconductor heterostructures such as quantum wells or quantum wires, is the 3D charge-carrier localization due to small SAQD sizes, which is comparable with the de Broglie wavelengths of electrons and holes. In order to calculate the charge carrier energy levels in an SAQD, we need to solve the 3D Schrödinger equation for a potential well formed by the SAQD band alignment. The simplest way is a calculation in the simple band approach, when charge carriers are considered as quasi-particles and where the effective mass and the interband interaction is not accounted. However, the interband interaction might result in a shift of energy levels, and it may be significant. The interaction between *Г* electrons and heavy-, light- and spin-splitting holes can be taken into account in the framework of the 8-band *k* × *p* approach [72]. We perform the test calculation of energy levels in the unstrained GaSb/AlP SAQD for different sizes using simple band and 8-band *k* × *p* approaches for comparison. The obtained results are shown in Figure 7.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 9 of 22

drostatic and the biaxial strains (**c**) are presented.

*2.5. Energy Levels* 

**Figure 7.** Energy levels for the ground state *Г* electrons and holes in unstrained GaSb/AlP SAQDs as a function of SAQD height. The calculation was performed in the simple band approach (red line-dots) and in the 8-band *k* × *p* approach (blue line-dots). The horizontal dashed lines show the band edge energies of the *Г* valley of the conduction band and the heavy hole sub-band for GaSb. The energy difference between the hole states, calculated in different approaches, is presented in the inset. **Figure 7.** Energy levels for the ground state electrons and holes in unstrained GaSb/AlP SAQDs as a function of SAQD height. The calculation was performed in the simple band approach (red line-dots) and in the 8-band *k* × *p* approach (blue line-dots). The horizontal dashed lines show the band edge energies of the valley of the conduction band and the heavy hole sub-band for GaSb. The energy difference between the hole states, calculated in different approaches, is presented in the inset.

We need to note that the calculations were performed taking into account *Г* electrons' states and heavy-, light- and spin-splitting holes' states into SAQDs, without a consideration of the *X* electrons' states into the AlP matrix. Nevertheless, in the comparison of the energy of *Г* electrons with the *X* band edge in AlP shows, the ground electron We need to note that the calculations were performed taking into account electrons' states and heavy-, light- and spin-splitting holes' states into SAQDs, without a consideration of the *X* electrons' states into the AlP matrix. Nevertheless, in the comparison of the energy of electrons with the *X* band edge in AlP shows, the ground electron states of unstrained GaSb/AlP SAQDs lie in the *X* valley of a conduction band of AlP. As is clearly seen from the curve behavior, the energy levels are shifted to the GaSb band edge in the SAQD, as shown in Figure 7 by dashed lines, with the increase in SAQD sizes. It is caused by reducing the quantum confinement effects. It is necessary to note that the difference in the electron energy level position, calculated in different approaches, exceeds 150 meV at the minimal SAQD height of 1 nm, and the value decreases with the dot size increase. It is topical to compare this energy difference with the uncertainty of material parameters reported for III–V compounds. The measurements of the GaSb direct bandgap at 300 K, performed by the photoreflectance and absorption spectroscopy techniques [75–77], yield the values in the range of 0.723–0.727 eV. Comparatively, VBO for the GaSb/AlP heterointerface is known with an accuracy of about 50 meV, as was discussed in [78]. Since this uncertainty is lower than the obtained energy difference, we conclude that, for a correct prediction of electron level position, the 8-band *k* × *p* approach is more useful. However, as can be seen in Figure 7, the energy difference between the results found by the simple band and 8-band *k* × *p* approaches for hole states is about 26 meV at the minimal SAQD height and even falls down lower than 1 meV with a dot size increase. This difference (i) does not exceed the VBO uncertainty and (ii) is not so significant in comparison with the hole localization energy, which is about 1.2–1.65 eV. This allows for the conclusion that, for the hole state

energy calculation with the focus on *E*loc, simple band and 8-band *k* × *p* approaches yield close results. Taking into account the easier and faster calculations with the use of the simple band approach, just this model was used for the following calculations. *E*loc, simple band and 8-band *k* × *p* approaches yield close results. Taking into account the easier and faster calculations with the use of the simple band approach, just this model was used for the following calculations.

states of unstrained GaSb/AlP SAQDs lie in the *X* valley of a conduction band of AlP. As is clearly seen from the curve behavior, the energy levels are shifted to the GaSb band edge in the SAQD, as shown in Figure 7 by dashed lines, with the increase in SAQD sizes. It is caused by reducing the quantum confinement effects. It is necessary to note that the difference in the *Г* electron energy level position, calculated in different approaches, exceeds 150 meV at the minimal SAQD height of 1 nm, and the value decreases with the dot size increase. It is topical to compare this energy difference with the uncertainty of material parameters reported for III–V compounds. The measurements of the GaSb direct bandgap at 300 K, performed by the photoreflectance and absorption spectroscopy techniques [75–77], yield the values in the range of 0.723–0.727 eV. Comparatively, VBO for the GaSb/AlP heterointerface is known with an accuracy of about 50 meV, as was discussed in [78]. Since this uncertainty is lower than the obtained energy difference, we conclude that, for a correct prediction of *Г* electron level position, the 8-band *k* × *p* approach is more useful. However, as can be seen in Figure 7, the energy difference between the results found by the simple band and 8-band *k* × *p* approaches for hole states is about 26 meV at the minimal SAQD height and even falls down lower than 1 meV with a dot size increase. This difference (i) does not exceed the VBO uncertainty and (ii) is not so significant in comparison with the hole localization energy, which is about 1.2–1.65 eV. This allows for the conclusion that, for the hole state energy calculation with the focus on

#### *2.6. Material Parameters 2.6. Material Parameters*

The material parameters, such as lattice constants, elastic constants, VBO, bandgap energies for , *X* and *L* valleys, spin-orbit splitting energy, effective charge-carrier masses, hydrostatic and shear deformation potentials and band parameters for 8-band *k* × *p* calculations for AlP, GaP, InP, AlSb, GaSb and InSb, and corresponding bowing parameters for ternary alloys, which were used for calculations, were taken from [33,79–81]. All used parameters are presented in Tables S1 and S2 in the Supplementary Materials. The material parameters, such as lattice constants, elastic constants, VBO, bandgap energies for *Г*, *X* and *L* valleys, spin-orbit splitting energy, effective charge-carrier masses, hydrostatic and shear deformation potentials and band parameters for 8-band *k* × *p* calculations for AlP, GaP, InP, AlSb, GaSb and InSb, and corresponding bowing parameters for ternary alloys, which were used for calculations, were taken from [33,79–81]. All used parameters are presented in Tables S1 and S2 in the Supplementary Materials.

#### **3. Results 3. Results**

#### *3.1. Critical SAQD Sizes 3.1. Critical SAQD Sizes*

First of all, the critical SAQD sizes calculated for different quaternary alloy compositions are presented in Figure 8. First of all, the critical SAQD sizes calculated for different quaternary alloy compositions are presented in Figure 8.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 10 of 22

**Figure 8.** Dependences of *h*c on the Sb fraction (*y*) for different contents of group III element (*x*) in Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y* SAQDs embedded in the AlP matrix. **Figure 8.** Dependences of *h*<sup>c</sup> on the Sb fraction (*y*) for different contents of group III element (*x*) in Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* , In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs embedded in the AlP matrix.

As shown in the figure, increasing the Sb fraction in the SAQD composition leads to a drastic decrease in *h*c, and this is caused by the increase in related lattice constants mismatch. At the same time, *h*<sup>c</sup> is practically not changed with the variation in Ga fraction in Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs because of close lattice constants in the GaP and AlP and in the GaSb and AlSb pairs [33]. On the contrary, increasing the In content in In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs results in the appreciable *h*<sup>c</sup> reduction governed by the trend of lattice constants mismatch. Note that the *h*<sup>c</sup> value, for the most strained InSb, GaSb and AlSb SAQDs in the AlP matrix, is about 1.6, 2.6 and 2.6 nm, respectively. It is wellknown that the localization energy in the SAQDs decreases with the SAQD size reduction due to the quantum confinement effect and that Eloc also increases with the increase in the fraction of narrow bandgap material in the alloy composition. Based on the strong dependences of *h*<sup>c</sup> on the alloy composition (*x,y*), we expect a competition between the quantum confinement effect and the alloy composition effect in the determination of the hole energy level's position and, consequently, hole localization energy. This competition would manifest itelf in the nonmonotonic character of *E*loc (*x,y*) dependencies. However, our expectations are not justified, and the *E*loc (*x,y*) dependencies are monotonic in general, as will be demonstrated further.

#### *3.2. Strain Distribution and Band Alignment 3.2. Strain Distribution and Band Alignment*  The obtained critical SAQD sizes were used for the strain calculations. The calcu-

will be demonstrated further.

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 11 of 22

The obtained critical SAQD sizes were used for the strain calculations. The calculated strain distribution in GaSb0.65P0.35/AlP SAQD with the height of 4 nm is presented in Figure 9. As is shown below, this alloy composition provides the minimal elastic strain along with the *E*loc value sufficient for application in non-volatile memories (~1.50 eV [12,13]). As is clearly seen in Figure 9, the strain distribution is strongly heterogeneous, and the deformation is not localized in the SAQD bulk. This provides a partial strain relaxation into the SAQD and reduces absolute peak values of deformation tensor components down to *εxx* = 6.78% and *εzz* = 4.49%, compared to 6.83%, as governed by the lattice constants mismatch. The results are in good agreement with the III–V SAQD strains discussed in the literature [67–70]. Note that the strain distribution is not significantly changed by the alloy composition variation. lated strain distribution in GaSb0.65P0.35/AlP SAQD with the height of 4 nm is presented in Figure 9. As is shown below, this alloy composition provides the minimal elastic strain along with the *E*loc value sufficient for application in non-volatile memories (~1.50 eV [12,13]). As is clearly seen in Figure 9, the strain distribution is strongly heterogeneous, and the deformation is not localized in the SAQD bulk. This provides a partial strain relaxation into the SAQD and reduces absolute peak values of deformation tensor components down to *εxx* = 6.78% and *εzz* = 4.49%, compared to 6.83%, as governed by the lattice constants mismatch. The results are in good agreement with the III–V SAQD strains discussed in the literature [67–70]. Note that the strain distribution is not significantly changed by the alloy composition variation.

As shown in the figure, increasing the Sb fraction in the SAQD composition leads to a drastic decrease in *h*c, and this is caused by the increase in related lattice constants mismatch. At the same time, *h*c is practically not changed with the variation in Ga fraction in Ga*x*Al1−*x*Sb*y*P1−*y* SAQDs because of close lattice constants in the GaP and AlP and in the GaSb and AlSb pairs [33]. On the contrary, increasing the In content in In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y* SAQDs results in the appreciable *h*c reduction governed by the trend of lattice constants mismatch. Note that the *h*c value, for the most strained InSb, GaSb and AlSb SAQDs in the AlP matrix, is about 1.6, 2.6 and 2.6 nm, respectively. It is well-known that the localization energy in the SAQDs decreases with the SAQD size reduction due to the quantum confinement effect and that Eloc also increases with the increase in the fraction of narrow bandgap material in the alloy composition. Based on the strong dependences of *h*c on the alloy composition (*x,y*), we expect a competition between the quantum confinement effect and the alloy composition effect in the determination of the hole energy level's position and, consequently, hole localization energy. This competition would manifest itelf in the nonmonotonic character of *E*loc (*x,y*) dependencies. However, our expectations are not justified, and the *E*loc (*x,y*) dependencies are monotonic in general, as

**Figure 9.** Strain distributions calculated for GaSb0.65P0.35/AlP SAQD with the height of 4 nm: (**a**) 2D map of *εxx* component, (**b**) 2D map of *εzz* component and (**c**) *εxx* and *εzz* trends along the central vertical SAQD axis marked by a thin yellow dashed line in panel (**b**). **Figure 9.** Strain distributions calculated for GaSb<sup>0</sup> .65P<sup>0</sup> .35/AlP SAQD with the height of 4 nm: (**a**) 2D map of *εxx* component, (**b**) 2D map of *εzz* component and (**c**) *εxx* and *εzz* trends along the central vertical SAQD axis marked by a thin yellow dashed line in panel (**b**).

#### *3.3. Band Alignment and Localization Energy 3.3. Band Alignment and Localization Energy*

The calculated band lineups of GaSb0.65P0.35/AlP SAQD are presented in Figure 10. The band edge trends along the central SAQD axis for the *Г*, *X*z, *X*XY and *L* valleys of the conduction band and the heavy-, light- and spin-orbital splitting hole sub-bands are presented in the figure. The ground hole and electron states of the SAQD belong to the heavy hole band and the *X*XY valley of conduction band, respectively, forming a band alignment of type-I. It is known that the heterostructures with the band alignment of The calculated band lineups of GaSb0.65P0.35/AlP SAQD are presented in Figure 10. The band edge trends along the central SAQD axis for the , *X*z, *X*XY and *L* valleys of the conduction band and the heavy-, light- and spin-orbital splitting hole sub-bands are presented in the figure. The ground hole and electron states of the SAQD belong to the heavy hole band and the *X*XY valley of conduction band, respectively, forming a band alignment of type-I. It is known that the heterostructures with the band alignment of type-Ihave a potential that localizes electrons and holes into the central narrow-bandgap material, while the heterostructures with the band alignment of type-II can localize only one kind of charge-carriers, electrons or holes in the central SAQD region and, for nonlocalized carriers, the potential works as a barrier [82,83]. The variation in SAQD alloy composition and size shows that the ground hole state of SAQDs lies in the subband of heavy holes, independently of the SAQD parameters. However, the composition and/or size variations can lead to a shift in the ground electron state to the *X*<sup>Z</sup> valley of AlP conduction band, and it leads to the change in the type-I SAQD band alignment to type-II. It is necessary to note that the similar change in the heterostructure band alignment type was observed experimentalty for GaSb/GaP [28], GaAs/GaP [84] and InSb/AlAs [85] heterostrucrutes. Accordingly, the control of the type of heterostructure band alignment is important for the prediction of the absorption and recombination properties, which are governed by interband transitions. Since the present study is focused on the hole energy spectrum, a detailed determination of SAQD parameters controlling the band alignment type is beyond the scope of this work.

The localization energy *E*loc is determined as an energy difference between the ground hole state and AlP valence band edge with the minimal energy in the SAQD vicinity, as shown in Figure 10. The dependence of *E*loc on the Sb fraction (*y*) in Ga*x*Al1−*x*Sb*y*P1−*y*,

In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs, at several fixed Ga or In fractions (*x*), is presented in Figure 11. cused on the hole energy spectrum, a detailed determination of SAQD parameters controlling the band alignment type is beyond the scope of this work.

type-I have a potential that localizes electrons and holes into the central narrow-bandgap material, while the heterostructures with the band alignment of type-II can localize only one kind of charge-carriers, electrons or holes in the central SAQD region and, for nonlocalized carriers, the potential works as a barrier [82,83]. The variation in SAQD alloy composition and size shows that the ground hole state of SAQDs lies in the subband of heavy holes, independently of the SAQD parameters. However, the composition and/or size variations can lead to a shift in the ground electron state to the *X*Z valley of AlP conduction band, and it leads to the change in the type-I SAQD band alignment to type-II. It is necessary to note that the similar change in the heterostructure band alignment type was observed experimentalty for GaSb/GaP [28], GaAs/GaP [84] and InSb/AlAs [85] heterostrucrutes. Accordingly, the control of the type of heterostructure band alignment is important for the prediction of the absorption and recombination properties, which are governed by interband transitions. Since the present study is fo-

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 12 of 22

**Figure 10.** Calculated band alignment for the GaSb0.65P0.35/AlP SAQD. **Figure 10.** Calculated band alignment for the GaSb<sup>0</sup> .65P<sup>0</sup> .35/AlP SAQD.

**Figure 11.** *E*loc (*y*) dependences for different contents of group III elements, as calculated for Ga*x-*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y* SAQDs embedded in the AlP matrix. Horizontal dashed lines indicate the energy range of *E*loc = 1.35–1.5 eV required for 10 years of hole storage [12,13,32,34]. **Figure 11.** *E*loc (*y*) dependences for different contents of group III elements, as calculated for Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* , In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs embedded in the AlP matrix. Horizontal dashed lines indicate the energy range of *E*loc = 1.35–1.5 eV required for 10 years of hole storage [12,13,32,34].

As is evident from the curve observation, with the Sb fraction increase, *E*loc monotonically increases in all three systems, and a value as high as ~2.04 eV is observed for pure GaSb/AlP SAQDs. The increase in Ga and In contents in Ga*x*Al1−*x*Sb*y*P1−*y* and In*x-*Al1−*x*Sb*y*P1−*y* SAQDs, respectively, also results in the *E*loc increase. These results indicate that the variation in *E*loc value is mainly determined by the change in alloy composition due to the changes in VBO. Indeed, as was shown by the SAQD critical size calculations, the increase in the fraction of narrow band gap material (InSb or GaSb) in the alloy is accompanied by a reduction in *h*c. Nevertheless, the continuous *E*loc growth with the in-As is evident from the curve observation, with the Sb fraction increase, *E*loc monotonically increases in all three systems, and a value as high as ~2.04 eV is observed for pure GaSb/AlP SAQDs. The increase in Ga and In contents in Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs, respectively, also results in the *E*loc increase. These results indicate that the variation in *E*loc value is mainly determined by the change in alloy composition due to the changes in VBO. Indeed, as was shown by the SAQD critical size calculations,the increase in the fraction of narrow band gap material (InSb or GaSb) in the alloy is accompanied by a reduction in *h*c. Nevertheless, the continuous *E*loc growth with the

crease in Sb or Ga/In fraction is observed in Figure 11, and it indicates a relatively weak role of the quantum confinement effect in the formation of the SAQD energy spectrum

nant because the energy position of the SAQD valence band top is proportional to the alloy composition [33]. The sublinear behavior of the *E*loc (*y*) functions observed for the InSb*y*P1−*y*/AlP SAQDs at *y* > 0.6 may be explained by a weak contribution of the quantum confinement effect for SAQDs with *h*c < 2.5 nm. In the case of In*x*Ga1−*x*Sb*y*P1−*y* SAQDs, the *E*loc (*y*) dependence changes the character smoothly from GaSb*y*P1−*y* to InSb*y*P1−*y* with an *x* increase. Note that, for *y* > 0.8, *E*loc is decreased, with a rise of the In content in an SAQD.

Let us discuss the calculated results in the light of a possible application of the SAQDs under consideration in non-volatile memory cells. As was shown, SAQDs formed in the InGaSb/AlP heterosystem are characterized by a high hole localization energy up to 2.04 eV, and, accordingly, they are prospective objects for non-volatile memory cells. The variations in solid alloy compositions and sizes of SAQDs allow us to estimate the

First of all, we need to compare two extreme cases of GaSb/AlP and InSb/AlP SAQDs. As was obtained, GaSb/AlP SAQD, with the height of 2.6 nm and base lateral size of 10.4 nm, is characterized by *E*loc = 2.04 eV, while the 1.6 nm high and 6.4 nm wide InSb/AlP SAQD has *E*loc = 1.82 eV. The lower localization energy in the InSb/AlP SAQD is caused by a lower valence band discontinuity and stronger quantum confinement effect, as is clearly seen in Figure 12, where the corresponding band diagrams are given. The higher *E*loc value, in combination with a significantly lower lattice mismatch (10.5% in GaSb/AlP vs. 15.6% in InSb/AlP [33]), indicates that GaSb/AlP SAQDs are more attractive

**4. Discussion** 

optimal SAQDs configuration.

increase in Sb or Ga/In fraction is observed in Figure 11, and it indicates a relatively weak role of the quantum confinement effect in the formation of the SAQD energy spectrum due to the high effective mass values for heavy holes. Thus, the nearly linear shape of the *E*loc (*y*) dependences is governed by the alloy composition variation. This factor is dominant because the energy position of the SAQD valence band top is proportional to the alloy composition [33]. The sublinear behavior of the *E*loc (*y*) functions observed for the InSb*y*P1−*y*/AlP SAQDs at *y* > 0.6 may be explained by a weak contribution of the quantum confinement effect for SAQDs with *h*<sup>c</sup> < 2.5 nm. In the case of In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs, the *E*loc (*y*) dependence changes the character smoothly from GaSb*y*P1−*<sup>y</sup>* to InSb*y*P1−*<sup>y</sup>* with an *x* increase. Note that, for *y* > 0.8, *E*loc is decreased, with a rise of the In content in an SAQD.

#### **4. Discussion**

Let us discuss the calculated results in the light of a possible application of the SAQDs under consideration in non-volatile memory cells. As was shown, SAQDs formed in the InGaSb/AlP heterosystem are characterized by a high hole localization energy up to 2.04 eV, and, accordingly, they are prospective objects for non-volatile memory cells. The variations in solid alloy compositions and sizes of SAQDs allow us to estimate the optimal SAQDs configuration.

First of all, we need to compare two extreme cases of GaSb/AlP and InSb/AlP SAQDs. As was obtained, GaSb/AlP SAQD, with the height of 2.6 nm and base lateral size of 10.4 nm, is characterized by *E*loc = 2.04 eV, while the 1.6 nm high and 6.4 nm wide InSb/AlP SAQD has *E*loc = 1.82 eV. The lower localization energy in the InSb/AlP SAQD is caused by a lower valence band discontinuity and stronger quantum confinement effect, as is clearly seen in Figure 12, where the corresponding band diagrams are given. The higher *E*loc value, in combination with a significantly lower lattice mismatch (10.5% in GaSb/AlP vs. 15.6% in InSb/AlP [33]), indicates that GaSb/AlP SAQDs are more attractive for the creation of non-volatile memory cells. However, from the technological point of view, it is very difficult to prepare pure GaSb SAQDs embedded into the AlP matrix due to the unavoidable material intermixing during the SAQD formation [28] and the risk of plastic relaxation of the strain [86]. Moreover, according to the predictions of the hole storage time [12,13,32,34], the value of *E*loc ~ 2 eV corresponds to the giant storage times of 108–10<sup>12</sup> years at room temperature, depending on the hole capture cross-section. Such giant storage times (>10 years) are evidently redundant for non-volatile memories. Thus, without loss of memory functionality, an appropriate reduction in *E*loc by the material intermixing is acceptable, with evident benefits of decreasing the SAQD strains. Thus, let us try to estimate the optimal SAQD configuration under the constraints of required storage time of 10 years and a minimal strain. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 14 of 22 for the creation of non-volatile memory cells. However, from the technological point of view, it is very difficult to prepare pure GaSb SAQDs embedded into the AlP matrix due to the unavoidable material intermixing during the SAQD formation [28] and the risk of plastic relaxation of the strain [86]. Moreover, according to the predictions of the hole storage time [12,13,32,34], the value of *E*loc ~ 2 eV corresponds to the giant storage times of 108–1012 years at room temperature, depending on the hole capture cross-section. Such giant storage times (>10 years) are evidently redundant for non-volatile memories. Thus, without loss of memory functionality, an appropriate reduction in *E*loc by the material intermixing is acceptable, with evident benefits of decreasing the SAQD strains. Thus, let us try to estimate the optimal SAQD configuration under the constraints of required storage time of 10 years and a minimal strain.

shown with blue dots.

**Figure 12.** Valence band top diagrams and energy levels calculated for GaSb/AlP (red lines) and InSb/AlP (blue lines) SAQDs with critical sizes. **Figure 12.** Valence band top diagrams and energy levels calculated for GaSb/AlP (red lines) and InSb/AlP (blue lines) SAQDs with critical sizes.

where *T* is the temperature, *σ*inf is the capture cross-section at a high temperature and γ is the coefficient independent of temperature. Localization energies of 1.35–1.50 eV are high enough for the hole storage times of ~10 years, depending on the capture cross-section *σ*inf which varied in the range of 10−12–10−9 cm2 in GaSb/GaP [29], InGaAs/GaP [27] and InGaSb/GaP [31] SAQDs, according to the available experimental results. Since the hole capture cross-section in SAQD is determined not only by the SAQD sizes but also by the hole–phonon interaction efficiency, Auger scattering and other factors [29], the prediction of the σinf value for the SAQD with specified alloy composition and size is a complicated task. Therefore, to simplify the task, the SAQDs were considered with an *E*loc value lying in the range of 1.35–1.50 eV and with the critical dot size. The possible variation in σinf was not accounted for in the calculations. In Figure 11, the horizontal dashed lines designate the targeted *E*loc range. Crossing these lines with *E*loc (*y*) curves determined for different *x* values spotlights a possibility to estimate the alloy composition (*x,y*) related to the targeted *E*loc level. In Figure 13, the composition parameters (*x,y*) for Ga*x-*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y* SAQDs obtained by this algorithm are

inf <sup>2</sup> *γT σ e*

= (11)

*kT E*

*a*

According to [12,13], the hole storage time can be estimated by relation:

*t*

*s*

According to [12,13], the hole storage time can be estimated by relation:

$$t\_s = \frac{e^{\frac{E\_g}{kT}}}{\gamma T^2 \sigma\_{\text{inf}}} \tag{15}$$

where *T* is the temperature, *σ*inf is the capture cross-section at a high temperature and γ is the coefficient independent of temperature. Localization energies of 1.35–1.50 eV are high enough for the hole storage times of ~10 years, depending on the capture cross-section *σ*inf which varied in the range of 10−12–10−<sup>9</sup> cm<sup>2</sup> in GaSb/GaP [29], InGaAs/GaP [27] and InGaSb/GaP [31] SAQDs, according to the available experimental results. Since the hole capture cross-section in SAQD is determined not only by the SAQD sizes but also by the hole–phonon interaction efficiency, Auger scattering and other factors [29], the prediction of the σinf value for the SAQD with specified alloy composition and size is a complicated task. Therefore, to simplify the task, the SAQDs were considered with an *E*loc value lying in the range of 1.35–1.50 eV and with the critical dot size. The possible variation in σinf was not accounted for in the calculations. In Figure 11, the horizontal dashed lines designate the targeted *E*loc range. Crossing these lines with *E*loc (*y*) curves determined for different *x* values spotlights a possibility to estimate the alloy composition (*x,y*) related to the targeted *E*loc level. In Figure 13, the composition parameters (*x,y*) for Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs obtained by this algorithm are shown with blue dots.

As is seen in Figure 13, in all alloys under consideration, *y* decreases on the *x* increase. The increase in *x* from 0 to 1 induces the *y* decrease from 1 to 0.55/0.65 in Ga*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and from 1 to 0.3/0.5 in In*x*Al1−*x*Sb*y*P1−*y*, for *E*loc fixed at 1.35 or 1.50 eV, respectively. As to the In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* solid solution, the *x* variation from 0 to 1 results in the *y* decrease from 0.5 to 0.3 or from 0.65 to 0.5, depending on the *E*loc value fixed at 1.35 or 1.50 eV, respectively. The dependences of the lattice constants mismatch *f* in the SAQD alloys and AlP matrix on the *x* value are also presented in Figure 13, and they are marked with red dot-lines. The behavior of *f* with the *x* variation in different alloys is principally different. Indeed, in Ga*x*Al1−*x*Sb*y*P1−*y*/AlP, the absolute *f* value reduces monotonically from 10.5–10% to 6–7%, depending on the *E*loc value, on the *x* variation from 0 to 1. The minimal absolute *f* values correspond to GaSb*y*P1−*y*/AlP SAQDs, with *y* lying in the range of 0.55–0.65. Note that these absolute *f* values of 6–7% are close to the lattice constants mismatch in the well-known InAs/GaAs SAQDs [33]. This fact is promising for the epitaxial growth of GaSb*y*P1−*y*/AlP SAQDs because the lattice mismatch is one of the important parameters controlling the possibility of SAQD formation. The absolute lattice mismatch levels in InxAl1-xSbyP1-y SAQD are as high as 10–12%, and they are weakly dependent on (*x*,*y*) values, as is clear in Figure 13. This effect is in a good agreement with the higher strain in the InSb/AlP system in reference to that in the GaSb/AlP system, as was discussed above. Moreover, in In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQD, the absolute *f* value increases up to 9.5–11.5% at *x* = 1, as shown in the bottom panel in Figure 13. Thus, the calculations allow us to point to the GaSb*y*P1−*y*/AlP SAQD with *y* = 0.55–0.65, height of 4.0–4.5 nm and a base size of about 16–18 nm as the optimal configuration with minimal strain for providing the required *E*loc = 1.35–1.50 eV.

It is necessary to discuss the perspectives of the epitaxial GaSbP/AlP SAQD growth. The novel GaSb/AlP heterosystem is most similar to the more investigated GaSb/GaP system. As was mentioned in [28,29,41], the GaSb deposition on GaP results in the GaSbP/GaP SAQD formation, with the Sb fraction lying in the range of 0.3–0.7, depending on the growth conditions. This information is optimistic for the successful growth of the GaSbP/AlP SAQDs with the required Sb content. Moreover, as shown above, the optimal configuration of GaSbP/AlP SAQDs with Sb content in the range of 0.55–0.65 is characterized by the *f* level being close to the lattice mismatch observed in the well-known InAs/GaAs heterosystem, where the perfectly strained SAQDs had already been obtained. However, some difficulties in the fabrication of the GaSbP/AlP SAQDs can be assumed due to the Al-Ga intermixing during the SAQD formation.

**Figure 13.** Sb fraction (*y*) as a function of group III element content (*x*) for the SAQD quaternary alloy (blue dots) calculated for the *E*loc value equal to 1.35 (thin dot-lines) and 1.50 eV (thick dot-lines). Red dot-lines give the SAQD/matrix lattice constant mismatch *f* as a function of *x* with a corresponding *y* fraction. **Figure 13.** Sb fraction (*y*) as a function of group III element content (*x*) for the SAQD quaternary alloy (blue dots) calculated for the *E*loc value equal to 1.35 (thin dot-lines) and 1.50 eV (thick dot-lines). Red dot-lines give the SAQD/matrix lattice constant mismatch *f* as a function of *x* with a corresponding *y* fraction.

As is seen in Figure 13, in all alloys under consideration, *y* decreases on the *x* increase. The increase in *x* from 0 to 1 induces the *y* decrease from 1 to 0.55/0.65 in Ga*x-*Al1−*x*Sb*y*P1−*y* and from 1 to 0.3/0.5 in In*x*Al1−*x*Sb*y*P1−*y*, for *E*loc fixed at 1.35 or 1.50 eV, respectively. As to the In*x*Ga1−*x*Sb*y*P1−*y* solid solution, the *x* variation from 0 to 1 results in the *y* decrease from 0.5 to 0.3 or from 0.65 to 0.5, depending on the *E*loc value fixed at 1.35 or 1.50 eV, respectively. The dependences of the lattice constants mismatch *f* in the SAQD alloys and AlP matrix on the *x* value are also presented in Figure 13, and they are marked with red dot-lines. The behavior of *f* with the *x* variation in different alloys is principally different. Indeed, in Ga*x*Al1−*x*Sb*y*P1−*y*/AlP, the absolute *f* value reduces monotonically from 10.5–10% to 6–7%, depending on the *E*loc value, on the *x* variation from 0 to 1. The minimal absolute *f* values correspond to GaSb*y*P1−*y*/AlP SAQDs, with *y* lying in the range of 0.55–0.65. Note that these absolute *f* values of 6–7% are close to the lattice constants mismatch in the well-known InAs/GaAs SAQDs [33]. This fact is promising for the epitaxial growth of GaSb*y*P1−*y*/AlP SAQDs because the lattice mismatch is one of the important parameters controlling the possibility of SAQD formation. The absolute lattice mismatch levels in InxAl1-xSbyP1-y SAQD are as high as 10–12%, and they are weakly de-Furthermore, the experimental data related to the formation of GaSb/GaP and GaAs/GaP SAQDs show a possibility of an exotic plastic strain relaxation mode. According to [84,86,87], at some growth conditions, a strain relaxation appeared due to the introduction of a system of 90◦ Lomer dislocations without 60◦ components. In this case, the dislocations lie at the interfaces, and they do not cross the SAQD bulk. Moreover, as was discussed in [88], the Lomer dislocation core does not contain dangling bonds, and that frees it from the deep level formation. The SAQD heterostructures, considered in [84,86,87], demonstrate a high luminescence intensity along with the radiative exciton recombination into SAQDs, and that confirms the absence of defect levels in and around SAQDs. Accordingly, it is expected that the SAQD system, where this strain relaxation mode is realized, may provide a long charge carrier storage time at appropriate *E*loc values. It can be reasonably assumed that a similar strain relaxation mode can be realized in GaSb/AlP and InSb/AlP heterosystems. Thus, the calculations of *E*loc for unstrained GaSb/AlP and InSb/AlP SAQDs are also interesting. Taking into account that this type of plastic relaxation leads to almost 100% relaxation of elastic deformations [84,86,87], the case of partial relaxation was not considered in this work.

pendent on (*x*,*y*) values, as is clear in Figure 13. This effect is in a good agreement with the higher strain in the InSb/AlP system in reference to that in the GaSb/AlP system, as was discussed above. Moreover, in In*x*Ga1−*x*Sb*y*P1−*y* SAQD, the absolute *f* value increases up to 9.5–11.5% at *x* = 1, as shown in the bottom panel in Figure 13. Thus, the calculations The calculations were performed for a truncated pyramid SAQD consisting of pure GaSb and InSb in the AlP matrix. Since the calculation was implemented for the unstrained SAQDs, the strain effects were not accounted for. The energy level's position was calculated in the framework of the simple band approach. The band lineup diagram of unstrained

GaSb/AlP SAQD was already provided in Figure 6a. This one, for the InSb/AlP system, is presented in Figure 14a. In the diagrams, it is clearly seen that these lineups are very similar, especially in the valence band part, and this is explained by the close values of VBO for the unstrained GaSb/AlP and InSb/AlP heterointerfaces [33]. The hole localization energy in the unstrained GaSb/AlP and InSb/AlP SAQDs lies in the range of 1.30–1.75 eV (see Figure 14b), which makes these SAQDs interesting objects for non-volatile memories, along with the strained InGaSb/AlP SAQDs. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 17 of 22

**Figure 14.** (**a**) Band alignment for the unstrained InSb/AlP SAQD. (**b**) The dependence of *E*loc on the SAQD height in the unstrained InSb/AlP SAQD. **Figure 14.** (**a**) Band alignment for the unstrained InSb/AlP SAQD. (**b**) The dependence of *E*loc on the SAQD height in the unstrained InSb/AlP SAQD.

Additionally, it should be noted that the considered InGaSb/AlP SAQDs might be attributed to the novel type of semiconductor low-dimensional heterostructures with the band alignment of type-I and indirect bandgap in some alloy compositions. These SAQDs are of interest as objects for investigations of localized exciton spin dynamics [89,90] due to the extremely long radiative lifetime of indirect excitons [91] lying in the microsecond range. As was demonstrated in [89], the fast bulk spin relaxation mechanisms are suppressed for trions in SAQDs, and this resulted in long, up to 30 μs, spin relaxation times. The coexistence of >10 years of hole storage time and microsecond exciton spin relaxation time in one structure opens the way for the creation of novel prospective hybrid memory devices based on a positive trion into SAQDs, combining a long charge storage in the floating gate with fast data processing using a trion spin. Additionally, it should be noted that the considered InGaSb/AlP SAQDs might be attributed to the novel type of semiconductor low-dimensional heterostructures with the band alignment of type-I and indirect bandgap in some alloy compositions. These SAQDs are of interest as objects for investigations of localized exciton spin dynamics [89,90] due to the extremely long radiative lifetime of indirect excitons [91] lying in the microsecond range. As was demonstrated in [89], the fast bulk spin relaxation mechanisms are suppressed for trions in SAQDs, and this resulted in long, up to 30 µs, spin relaxation times. The coexistence of >10 years of hole storage time and microsecond exciton spin relaxation time in one structure opens the way for the creation of novel prospective hybrid memory devices based on a positive trion into SAQDs, combining a long charge storage in the floating gate with fast data processing using a trion spin.

#### **5. Conclusions 5. Conclusions**

The energy spectrum of novel InGaSb/AlP SAQDs was investigated theoretically with the focus on possible non-volatile memory applications. The detailed calculations of the energy spectra of strained Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*y* and In*x*Ga1−*x*Sb*y*P1−*y* SAQDs formed in the AlP matrix were performed for different alloy compositions and SAQD sizes. The variations were performed, keeping SAQD sizes as critical, with respect to the introduction of dislocations for different alloy compositions. It was theoretically elucidated that, among all SAQDs under consideration, the GaSbP/AlP SAQDs with the Sb fraction in the range of 0.55–0.65 have a minimal SAQD/matrix lattice constant mismatch and provided *E*loc of 1.35–1.50 eV. These *E*loc values are sufficient for non-volatile memory applications. This makes the GaSb/AlP heterosystem the most appropriate one for non-volatile memory cell fabrication. Additionally, the energy spectra of unstrained InSb/AlP and GaSb/AlP SAQDs were calculated. In these systems, the values of *E*loc up to 1.65–1.70 eV were predicted, which also makes these SAQDs suitable for non-volatile memory applications. The energy spectrum of novel InGaSb/AlP SAQDs was investigated theoretically with the focus on possible non-volatile memory applications. The detailed calculations of the energy spectra of strained Ga*x*Al1−*x*Sb*y*P1−*y*, In*x*Al1−*x*Sb*y*P1−*<sup>y</sup>* and In*x*Ga1−*x*Sb*y*P1−*<sup>y</sup>* SAQDs formed in the AlP matrix were performed for different alloy compositions and SAQD sizes. The variations were performed, keeping SAQD sizes as critical, with respect to the introduction of dislocations for different alloy compositions. It was theoretically elucidated that, among all SAQDs under consideration, the GaSbP/AlP SAQDs with the Sb fraction in the range of 0.55–0.65 have a minimal SAQD/matrix lattice constant mismatch and provided *E*loc of 1.35–1.50 eV. These *E*loc values are sufficient for non-volatile memory applications. This makes the GaSb/AlP heterosystem the most appropriate one for non-volatile memory cell fabrication. Additionally, the energy spectra of unstrained InSb/AlP and GaSb/AlP SAQDs were calculated. In these systems, the values of *E*loc up to 1.65–1.70 eV were predicted, which also makes these SAQDs suitable for non-volatile memory applications.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/nano12213794/s1, Table S1: Materials parameters for AlP, GaP, InP, AlSb, GaSb and InSb at 300 K, which were used for the calculations. *a*0—lattice constant, *C*11, *C*12, *C*44—elastic constants, *E<sup>g</sup>* ,*X*,*L*—bandgaps for , *X* and *L* valleys, *a* ,*X*,*L <sup>v</sup>*—hydrostatic deformation potentials for the conduction band edge in , *X* and *L* points of the Brillouin zone and valence band, *bX*,*v*—shear deformation potential for the conduction band at *X* point of the Brillouin zone and valence band, ∆0—energy of spin-orbital splitting in the valence band, VBO—valence band offsets, *m*—electron effective mass in the point of the Brillouin zone, *mXt* and *mXl*—transversal and longitudinal electron effective mass in the *X* point of the Brillouin zone, *mL*<sup>t</sup> and *mL*l—transversal and longitudinal electron effective mass in the *L* point of the Brillouin zone, *mhh*, *mlh*, *mSO*—effective masses for the heavy, light and spin-orbital splitting holes, *F*—Kane's parameter, *E*P—Kane's matrix element, *γ*1,2,3—Luttinger parameters for the valence band. Table S2: Bowing parameters for GaAlP, InGaP, AlInP, GaAlSb, InGaSb, AlInSb, AlSbP, GaSbP and InSbP [33]. Figure S1: Solving of the Equation (16) by the graphic method for the case of In0.5Ga0.5Sb0.5P0.5/AlP SAQD. Linear part of the equation depicted by the blue line, the logarithmic one by the red line. The black arrow points to the obtained hc value.

**Author Contributions:** Conceptualization, D.S.A.; methodology, D.S.A.; investigation, D.S.A.; writing—original draft preparation, D.S.A., V.V.A.; writing—review and editing, D.S.A., V.V.A.; visualization, D.S.A.; project administration, D.S.A.; funding acquisition, D.S.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Russian Science Foundation, grant 22-22-20031 https: //rscf.ru/project/22-22-20031/ (21 March 2022), and by the Novosibirsk Regional Government, grant No. r-14 (6 April 2022).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are available from the authors on request.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relations that could have appeared to influence the work reported in this paper.

#### **References**

